Question

Find the equation of the circle with the given characteristics: Center (-2, 3.5) and Radius 12.

a) (x + 2)² + (y - 3.5)² = 144
b) (x - 2)² + (y + 3.5)² = 144
c) (x + 2)² + (y + 3.5)² = 144
d) (x - 2)² + (y - 3.5)² = 144

Answer 1

The equation of a circle with center (-2, 3.5) and radius 12 is (x + 2)² + (y - 3.5)² = 144, which corresponds to option (a).

Step-by-step explanation:

To find the equation of a circle, you can use the standard form (x - h)² + (y - k)² = r², where (h,k) is the center of the circle and r is its radius.

Given that the center is (-2, 3.5) and the radius is 12, we substitute these values into the standard form:

(x + 2)² + (y - 3.5)² = 12²

Therefore, the equation of the circle with the given characteristics is:

(x + 2)² + (y - 3.5)² = 144

This corresponds to option (a).