Question

What is the equation for the circle centered at (-4, -6) with a radius of 3?

A) (x + 4)^2 + (y + 6)^2 = 9
B) (x - 4)^2 + (y - 6)^2 = 9
C) (x - 4)^2 + (y - 6)^2 = 3
D) (x + 4)^2 + (y + 6)^2 = 3

Answer 1

The correct equation of the circle centered at (-4, -6) with a radius of 3 is (x + 4)^2 + (y + 6)^2 = 9.

Step-by-step explanation:

The equation for a circle is generally given by the formula (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is its radius. For the circle centered at (-4, -6) with a radius of 3, we use these values in the formula to get:

(x - (-4))^2 + (y - (-6))^2 = 3^2

This simplifies to:

(x + 4)^2 + (y + 6)^2 = 9

This matches option A, which is the correct equation for the given circle.