Which equation represents a circle with a center at (-4,9) and a diameter of 10 units?
(x - 9)2 + (+ 4)2 = 25
(x + 4)2 + (- 9)2 = 25
(x - 9)2 + ( + 4)2 = 100
(x + 4)2 + (- 9)2 = 100
PLZ HELP!
Answers
The equation of circle with center at P ( -4 , 9 ) and diameter 10 units is given by ( x + 4 )² + ( y - 9 )² = 25
What is a Circle?A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the equation of circle be represented as A
Now , the value of A is
Let the center of the circle be P ( -4 , 9 )
Let the diameter of the circle be d = 10 units
So , the radius of the circle r = d/2 = 5 units
And , standard form of a circle is
( x - h )² + ( y - k )² = r²,
So , the equation of circle is
( x + 4 )² + ( y - 9 )² = 25
Hence , the equation of circle is ( x + 4 )² + ( y - 9 )² = 25
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hope this helps :)
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