Question

Which of the following answer choices is an equation for the circle with a center of (-2, 3) and a radius of 3?

A.x2 + y2 + 4x - 6y + 4 = 0
B.x2 + y2 + 4x - 6y + 22 =0
C.2x2 + 2y2 + 3x - 3y + 4 = 0
D.3x2 + 3y2 + 4x - 6y + 4 = 0

Answer 1

A

Explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (- 2, 3) and r = 3 , then

(x + 2)² + (y - 3)² = 9 ← expand left side using FOIL

x² + 4x + 4 + y² - 6y + 9 = 9 ( subtract 9 from both sides )

x² + y² + 4x - 6y + 4 = 0 → A