Mathematics High School

Writing an equation of an ellipse given the foci and major axis length

Answers

Answer 1

Given

Major axis of length = 12

Foci at ( 9 ,1 ) and ( -1, 1 )

Find

Equation of an ellipse

Explanation

As we know , major axis = 2a = 12

thus a = 6

the midpoint between the foci is the center , so

[tex]\begin{gathered} C:(\frac{8}{2},\frac{2}{2}) \\ C:(4,2) \end{gathered}[/tex]

the distance between the foci is equal to 2c

[tex]\begin{gathered} 2c=\sqrt{\left(9+1\right)^2+0^2} \\ 2c=10 \\ c=5 \end{gathered}[/tex]

now,

[tex]\begin{gathered} c^2=a^2-b^2 \\ b^2=a^2-c^2 \\ b^2=36-25 \\ b^2=11 \end{gathered}[/tex]

so , the equation of an ellipse is

[tex]\begin{gathered} \frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2} \\ \frac{(x-4)^2}{11}+\frac{(y-2)^2}{36} \end{gathered}[/tex]

Final Answer

The equation of an ellipse

[tex]\frac{(x-4)^{2}}{11}+\frac{(y-2)^{2}}{36}[/tex]

Related Questions

Please help,

A map of an amusement park is shown on the coordinate plane with the approximate location of several rides.

Determine the distance between the Woozy Wheel and the Roller Rail.

A. 119 units
B. 11 units
C. 169 units
D. 13 units

Answers

Answer:

D. 13 units

Step-by-step explanation:

Woozy Wheel: (-14, 1)

Roller Rail: (-2, -4)

[tex] \sqrt{ { - 14 - ( - 2))}^{2} + {(1 - ( - 4))}^{2} } [/tex]

[tex] \sqrt{ {( - 12)}^{2} + {5}^{2} } [/tex]

[tex] \sqrt{144 + 25} = \sqrt{169} = 13[/tex]

The distance between the Woozy Wheel and the Roller Rail is D. 13 units

What is the distance formula between two points?

The distance formula between two points (x₁, y₁) and (x₂, y₂) is

D = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].

Given, A map of an amusement park is shown on the coordinate plane with the approximate location of several rides.

The point at which Woozy Wheel is (-14, 1) and the point at which Roller Rail

is (-2, - 4).

∴ The distance between the Woozy Wheel and the Roller Rail is,

D = [tex]\sqrt{(-2 + 14)^2 + (-4 - 1)^2}[/tex] units.

D = [tex]\sqrt{(12)^2 + (-5)^2}[/tex] units.

D = [tex]\sqrt{144 + 25}[/tex] units.

D = [tex]\sqrt{169}[/tex] units.

D = 13 units.

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Three students that share a townhouse find that their electric bill for October is $5.29 less than the September bill. The total of both bills is $155.93, and each bill is split evenly among the roommates how much they each owe in September?

Answers

We will have the following:

From the problem we will have the following expressions:

[tex]\begin{gathered} S=x \\ O=x-5.29 \\ S+O=155.93 \\ 2x-5.29=155.93 \end{gathered}[/tex]

Now, from this we determine the value for the bill on september:

[tex]\Rightarrow2x=161.22\Rightarrow x=80.61[/tex]

Now, since there are 3 people, the payment for each one is:

[tex]\frac{80.61}{3}=26.87[/tex]

So, the payment for each one is $26.87 in September.

for each equation complete the table and then graph the equation

Answers

The slope-intercept form a of the equation of a line is:

[tex]y=mx+b[/tex]

Where m is the slope and b is the intercept.

For this exercise m = -1 and b = -1

To find the 'y' values of the table you just have to replace the x values into the equation:

And put these pairs into the graph and join them with a line:

Wukong and Nice are playing a soccer match
and the probabilities of them scoring are7/8 and 5/6 respectively. What is the probability that at
least one of them will score a goal if they each
play the ball once?

Answers

The probability that at least one of them will score a goal if they each play the ball once is 47/48.

What is probability?

Probability is a mathematical and scientific term that describes the possibility or occurrence of an event. Many events are difficult to predict with absolute accuracy. Only the likelihood of an event occurring, i.e. how likely it is, can be predicted using probability.

Given:

The probabilities of Wukong and Nice scoring in the match are 7/8 and 5/6 respectively.

The probability that at least one of them will score a goal is,

= 1 - P(both of them not scoring a goal)

So the probability of Wukong and Nice not scoring a goal in the match is,

(1 - 7/8) (1 - 5/6) = (1/8)(1/6) = 1/48

Now the required probability is,

= 1 - P(both of them not scoring a goal)

= 1 - 1/48

= 47/48

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Last year, Raina had $10,000 to invest. She invested some of it in an account that paid 7% simple interest per year, and she invested the rest in an account that paid 6% simple interest per year. After one year, she received a total of $620 in interest. How much did she invest in each account?

Answers

If after one year, she received a total of $620 in interest. The amount that she invest in each account is 2,000 amount invested at 7% , 8,000 amount invested at 6.

Amount invested

Let x represent the amount invested

Hence,

.07x + .06(10,000-x) =620

.07X+600-.06x = 620

Combine like terms

.01x =620-600

.01x=20

Divide both side by .01x

x=20/.01

x =2,000 amount invested at 7%

So,

10,000-2,000 = 8,000 amount invested at 6%

Check :

.07 × 2,000+.06× 8,000=620

150 + 480 = 620

620 = 620

Therefore we can conclude that $2,000 was invested at 7% and $8,000 was invested at 6%.

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3x6 = 7x - 8
What equations have the same solution set?

Answers

If u don’t know the answer it’s 211 and I recommend having parentheses on 3x6 and a divide 7x-8

Find the number which wohen added
to its square, makes 90..

Answers

Answer: -10 or 9

Step-by-step explanation:

Let the number be x. Then,

[tex]x^2 +x=90\\\\x^2 +x-90=0\\\\(x+10)(x-9)=0\\\\x=-10, 9[/tex]

23 out of 26 students want pancakes and the rest want waffles. What is the ratio of the number of students who want waffles to the total number of students?

Write your answer as two numbers separated by a colon (for example, 2:3).
please help asap!!!!

Answers

The ratio of the number of students who want waffles to the total number of students is 3 : 26 students

The ratio of the number of students who want waffles to the total number of students?

Ratio refers to the number representing a comparison between two named things or quantities.

Total number of students = 26Number of students who wants pancakes = 23

Number of students who wants waffles = Total number of students - Number of students who wants pancakes

= 26 students - 23 students

= 3 students

Ratio of the number of students who want waffles to the total number of students = 3 students : 26 students

So therefore, the ratio of the number of students who want waffles to the total number of students separated by a colon is 3 : 26

Answers

Answer:

Step-by-step explanation:

why? because there are 5 pieces in each building set so 5×8=40 so the answer is 40

Solve for x in the triangle. Round your answer to the nearest tenth.
20
X
52°
X =

Answers

Answer:

25.4

Step-by-step explanation:

use sine rule [tex]\frac{a}{sinA}[/tex]=[tex]\frac{b}{sinB}[/tex]

[tex]\frac{20}{sin(52)}[/tex] ×sin(90)

use sine rule [tex]\frac{opposite}{hypotenuse}[/tex] = sinФ

[tex]\frac{20}{h}[/tex]=sin(52)

rearrange-

20÷sin(52)=h

(h is x)

PLEASE ANSWER ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

The points -5 2/3 and 5 1/3 in the number line attached

How to solve an equation

An equation shows the relationship between two or more numbers and variables.

Number line a line containing numbers marked at intervals.

The mixed fraction -5 2/3 is equivalent to -[(5 * 3 + 2)/3] = -17/3

The mixed fraction 5 1/3 is equivalent to [(5 * 3 + 1)/3] = 16/3

The points -5 2/3 and 5 1/3 are represented

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Help please promise i'm Grade 2 and I don't know what is this but please help our teacher didn't teach us this.

Answers

Answer:

First one is 92

Step-by-step explanation:

Answer:

1. 9/2

2. 7 3/13

3. 3 13/15

4. 3 25/27

5. 2 1/4

6. 3 30/91

7. 2 5/21

8. 6 3/5

Step-by-step explanation:

When I put it like 2 5/21 I mean it's a mixed number.

Now I'll tell you the steps.

1. Find the common denominator (The denominator is the bottom number of the fraction. To find it you have to write out the multiplies of each number and once a number is the same that's the common denominator.)

2. Multiply the numerator by the amount of times it took to find the common denominator. (The numerator is the top number of the fraction. And the amount of times you'll have to multiply the numerator depends. I'll put an example below)

Example:

4/20 ÷ 7/2

2 goes into 20, 10 times so you have to multiply 7 by 10.

Then you'll get

70/20.

Now you can solve it.

4/20÷70/20

(I put random numbers so the answer may turn out funky this is just an example.)

3. Divide the fractions

4. Simplify answer if possible

I hope this helped!

What is the equation of the line that is perpendicular to the line y = -5x - 12 and passes through the
point (10, 4).

Answers

Line's equation is y=(1/5)x + 2.

What does perpendicular mean?

In elementary geometry, two geometrical objects are perpendicular if they intersect at a right angle. The condition of perpendicularity can be graphically represented using the perpendicular symbol,. Any pair of lines, any pair of planes, or any pair of lines and planes can be used to define it.

The arrow

In slope-intercept form, y=-5x12

y=mx+b

where the slope m is.

Thus, the slope of this line is

m= -5

Slopes on perpendicular lines are reciprocally negative. In other words, modify the sign by taking the slope's reciprocal.

The reciprocal of (-5) in the negative is 1/5.

Plug in the point to determine b in the formula y = (1/5)x + b.

4 = (1/5)(10) + b

4 = 2 + b

b = 2

The perpendicular line passing through the indicated point is y= (1/5)x + 2.

Thus, the equation of the line that is perpendicular to the line y = -5x - 12 and passes through the point is y= (1/5)x + 2.

point (10, 4). (10, 4).

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9 = 3y + 37 + 4y solve for y and simplify as much as possible

Answers

[tex]3y + 37 + 4y = 9 \\ 3y + 4y = 9 - 37 \\ 7y =- 28 \\ \frac{7y}{7} = \frac{-28}{7} \\ y = -4[/tex]

ATTACHED IS THE SOLUTION

Choose the graph of g(x) = |x-1| and its parent function f. Then choose the description of the
transformation.

Answers

top right corner is the graph and it is a shift to the right

The equation for line A is given by y = 1/2 x + 4 suppose line A is parallel to line B and line T is perpendicular to line A point (- 3, 1) lies on both lineB and liner T. Part A write an equation for line B Part B Write an equation for line T

Answers

We will find lines B &

View the image to answer the question.

Answers

Considering the table of f ( x ) and graph of g ( x ), the value of the expression [tex]\lim_{x \to 1} 2f(x)+g(x)^2[/tex] is represented by 3

How to determine the value when x tends to 1 using the graph and the table

The table represents the values of f ( x ). Using the table, checking the value of f ( x ) when x = 1 gives f ( x ) = 1

Using the graph, the value of g ( x ) when x = 1 is traced to give a value of -1

substituting the values of f ( x ) = 1 and g ( x ) = -1 into the equation

[tex]\lim_{x \to 1} 2f(x)+g(x)^2[/tex]

[tex]=\lim_{x \to 1} 2f(1)+g(1)^2[/tex]

[tex]=2(1)+(-1)^2[/tex]

= 2 + 1

= 3

This makes the third option the best choice and the value is 3

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What is Huangmei Opera, and where did Huangmei Opera originate?

Answers

Answer:

look at explanation!

Step-by-step explanation:

Huangmei Opera is a local opera of the Han nationality. Being one of Chinese big five operas, Huangmei Opera enjoy equal popularity with Beijing Opera, Yue Opera, Ping Opera and Yu Opera. It originates from Huangmei, a junction of Hubei, Anhui and Jiangxi.

is one of the five major opera genres in China. It is the main local opera in City, Anhui Province. The predecessor of Opera is and Anhui Opera. Also known as tune, in the middle and late Dynasty, tea picking tune was combined with local folk opera in Prefecture, Anhui Province, and sung and recited in dialect of , and gradually developed into a new type of opera, which was called at that time. This is the early stage The prototype of i Opera. Later, drew on the music, performances and repertoires of and , and began to perform "this opera". Later, with Town, County, Prefecture as the center, and after more than 100 years of development, it became an independent large-scale local drama - Anhui Opera, which was renamed " Opera" in the Opera is the main local opera variety in Anhui, and after spreading to the neighboring City, Jiangxi Province, and City, Hubei Province, it eventually became a well-known national opera variety. There are also professional and amateur performance groups of Opera in Taiwan and Taiwan, which are widely welcomed. After the founding of the People's Republic of China, it quickly developed into an influential opera genre in the whole of China and became famous overseas. In 2006, Opera was selected into the first batch of China's national intangible cultural heritage.

Step-by-step explanation:

Please help on 15 and 16.

Answers

Answer:

Step-by-step explanation:

please help
with answer

Answers

Answer: -20

Step-by-step explanation: 16 x 1/4 - 4x 6

Jennifer has a collection of weights that each weigh 4, 6, or 9 pounds. If altogether, the weights weigh 42 pounds, what is the largest number of weights Jennifer could own?

Answers

The largest number of weights Jennifer could own is 798.

When do we use multiplication?

Repeated addition of the same number is made easier by multiplying the numbers. When we need to merge groups of similar sizes, we employ it. For instance, if there are 5 baskets, each containing 4 apples, we can use multiplication to get the total number of apples, which is 5 x 4 = 20 apples.

We can rapidly determine the total number of things by multiplying. When multiplying, we'll consider the number of groups with similar sizes and the number of items in each group.

Given: The collection of weights : 4 , 6 and 9 pounds

The total weight of the weights = 42 pounds

Thus the largest number of weights jennifer could own is 4+6+9 = 19 multiplied by the total weight of the weights

= 19 × 42

= 798.

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What is the solution to the inequality x2 + 2x ≤ 24?

Answers

Answer:

-6 ≤ x ≤ ∨ x = 4

Step-by-step explanation:

x^2 + 2·x ≤ 24

x^2 + 2·x - 24 ≤ 0

-1 - √(1 + 24) ≤ x ≤ -1 + √(1 + 24)

-1 - 5 ≤ x ≤ -1 + 5

-6 ≤ x ≤ ∨ x = 4

Can someone please help me on this?

Answers

y = 4x-9
Reason: It goes up 4 each time and it started at -9.

Solve for X to the nearest tenth please help me asap

Answers

Answer:

10.4

Step-by-step explanation:

explanation in photos

Isaac performs at a fair he earns 100 dollars plus 3 dollars for every ticket sold he wants to earn more than 450 dollars. write an inequality to find the number of tickets that need to be sold for isaac to earn more than 450 dollars.

Answers

The inequality to find the number of tickets Isaac needs to sell to earn than $450 is 100 + 3x ≤ 450 and the number of times he will sell the tickets is 117.

What is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Inequality, A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.

So, the inequality can be:

Issac earns:-

By performing $100 and by selling each ticket $3.Let, this be $100 be constant.

Isaac wants to earn $450,

$100 he already has.3 × 117 = $351

So, the inequality that can be formed here is:

Let, 'x' be the number of times Isaac sell the tickets.

100 + 3x ≤ 450

By solving we will get:

100 + 3(117) ≤ 450100 + 351 ≤ 450451 < 450

Therefore, the inequality to find the number of tickets Isaac needs to sell to earn than $450 is 100 + 3x ≤ 450 and the number of times he will sell the tickets is 117.

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HELPPPP PLEASEEEE

If y varies directly with x, and y=18
when x=6
, find the value of y when x=4
.

Answers

Answer:

y=12

Step-by-step explanation:

1.Took the ratio between x and y value.

18:6 is the same as 3:1 ratio this means that our y value will be 3 times greater than our x value.

What is the equation of the line that passes through the point (5, 3) and has an
undefined slope?

Answers

The equation of the line will be expressed as x = 5.

Slope of a line may be defined as the steepness of a curve plotted on paper. The slope of a line between two points (x₁, y₁) and (x₂, y₂) can be calculated by formula m = (y₂ - y₁)/(x₂ - x₁).

If we have two points and we have to find equation of line through two points (x₁, y₁) then equation will be (y - y₁) = m(x - x₁) where m is the slope of line.

We have two points (5, 3) and slope is undefined.

Undefined slope can be expressed as 1/0. So, the equation of line through (5, 3) will be

(y - 3) = 1/0 (x - 5)

=> x - 5 =0

=> x = 5

This is the equation of line, and this line will be parallel to y-axis.

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5x+6y=37
2x + 3y = 4

Answers

Answer:

x = 29

y = -18

Step-by-step explanation:

5(29) + 6(-18) = 37

145 - 108 = 37

(x,y) = (29, - 18)
Hope that works

What's the best food you could eat?

Answers

Answer:

It unexpected, but did you know you could live over 40 years on just pizza! Crazy! It's not so good tho because of all the salt in it, so that's not THE HEALTHIEST. I've looked it up and, fish seems to be the top choice when it comes to what's good for you. I've also have come across dark green vegetables too.

Step-by-step explanation:

I didn't notice you were just talking about what tastes good rather than whats healthiest.... eh! YOUR NOW EDUCATED!!!

Hope it helps! =D

Bill Gutierrez drove 130 miles at a speed of 65 miles per hour on an expressway for 2 hours. He drove 67.5 miles for 1.5 hours at 45 miles per hours on a state highway. What is his average speed?

Answers

Bill's average speed throughout his journey is 55mi/hr

Average Speed

The average speed Bill drove can be calculated using the formula of speed which is given as

[tex]speed = \frac{distance}{time}[/tex]

Substituting all the values into the equation, we can find the speed.

130 miles at 65mi/hr, 67.5miles at 1.5 hours and 45mi/hr.

[tex]average speed = \frac{65 + 45}{2} = \\speed = \frac{110}{2} = 55mi/hr[/tex]

The average speed at the end of the journey is 55mi/hr

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