Question

What is the equation of the circle that has a center at (-3, 1) and a radius of 5? A) (x + 3)2 + (y - 1)2 = 5 B) (x - 3)2 + (y + 1)2 = 5 C) (x + 3)2 + (y - 1)2 = 25 D) (x - 3)2 + (y + 1)2 = 25

Answer 1

C

Explanation:

The vertex form of the equation of a circle is
`(x-h)^2 + (y-k)^2 = r^2` where (h,k) is the center of the circle and r is the radius. This means that for the circle with center (-3,1) and radius 5 substitute into the vertex form these values. Substitute h = -3, k= 1, and r = 5. The equation becomes
`(x--3)^2 + (y-1)^2 = 5^2`. This simplifies to
`(x+3)^2 + (y-1)^2 = 25`. The solution is C.