Question

A circle has its center at (-2, 5) and a radius of 4 units. What is the equation of the circle? Answer choices:

(A) (x + 2)2 + (y - 5)2 = 16
(B) (x + 2)2+ (y + 5)2= 16
(C) (x + 2)2+(y - 5)2 = 4
(D) (x - 2)2+(y + 5)2 = 4

Answer 1

option (a) is correct.

The equation of a circle has its center at (-2, 5) and a radius of 4 units. is
`(x+2)^2+(y-5)^2=16`

Explanation:

Given : A circle has its center at (-2, 5) and a radius of 4 units.

We have to choose the correct equation representing this given circle.

The general equation of circle with center (h , k) and radius 'r' is given by equation
`(x-h)^2+(y-k)^2=r^2`

For the given circle with center at (-2, 5) and a radius of 4 units.

that is h = -2 , k = 5 and r = 4 , we have,

`(x-h)^2+(y-k)^2=r^2` substitute, we have,

`(x-(-2))^2+(y-5)^2=(4)^2`

Simplify , we get,

`(x+2)^2+(y-5)^2=16`

Thus, option (a) is correct.

The equation of a circle has its center at (-2, 5) and a radius of 4 units. is
`(x+2)^2+(y-5)^2=16`

Answer 2

The equation of the circle:
( x - h )² + ( y - k )² = r²;
h = - 2, k = 5, r = 4
Answer:
A ) ( x + 2 )² + ( y - 5 )² = 16