Question

Enter the equation of the circle in standard form with the center and radius given.

Center: (-8, -3), Radius: 2 √ 3

a. (x + 8)² + (y + 3)² = 12
b. (x + 8)² + (y + 3)² = 36
c. (x - 8)² + (y - 3)² = 12
d. (x - 8)² + (y - 3)² = 36

Answer 1

The correct equation of the circle with center (-8, -3) and radius 2 √ 3 is (x + 8)² + (y + 3)² = 12, which is option a.

Step-by-step explanation:

The equation of a circle in standard form is given by (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. Given the center at (-8, -3) and a radius of 2 √ 3, we plug these values into the formula as follows:

(x - (-8))² + (y - (-3))² = (2 √ 3)²

This simplifies to:

(x + 8)² + (y + 3)² = 12

Therefore, the correct equation of the circle in standard form is option a. (x + 8)² + (y + 3)² = 12.