Question

In the coordinate plane, which equation describes the locus of points 5 units from the point (–2, 2)?

(x + 2)2 + (y – 2)2 = 5

(x – 2)2 + (y + 2)2 = 25

(x – 2)2 + (y + 2)2 = 5

(x + 2)2 + (y – 2)2 = 25

Answer 1

This is a circle centered at (-2,2) with radius 5.

center = (h,k) = (-2,2) so h = -2 and k = 2

radius = r = 5

The equation of any circle is (x-h)^2 + (y-k)^2 = r^2

Plug the three values mentioned into that equation

(x-h)^2 + (y-k)^2 = r^2

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

(x+2)^2 + (y-2)^2 = 25

Answer: Choice D

Answer 2

This is a circle centered at (-2,2) with radius 5.

center = (h,k) = (-2,2) so h = -2 and k = 2
radius = r = 5

The equation of any circle is (x-h)^2 + (y-k)^2 = r^2

Plug the three values mentioned into that equation
(x-h)^2 + (y-k)^2 = r^2
(x-(-2))^2 + (y-2)^2 = 5^2
(x+2)^2 + (y-2)^2 = 25

Answer: Choice D