Question

Write an equation of a circle with the center at (-6,4) and a diameter of 6.

a) (x + 6)^2 + (y - 4)^2 = 9
b) (x - 6)^2 + (y + 4)^2 = 9
c) (x + 6)^2 + (y - 4)^2 = 36
d) (x - 6)^2 + (y + 4)^2 = 36

Answer 1

The correct equation for a circle with a center at (-6, 4) and a diameter of 6 is (x + 6)² + (y - 4)² = 9, which is option a).

Step-by-step explanation:

The question asks us to write an equation of a circle with a center at (-6, 4) and a diameter of 6. The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius of the circle. Since the diameter is 6, the radius is half of that, which is 3. Therefore, our equation will have a radius squared, or 3², which is 9. The correct equation for the circle is (x + 6)² + (y - 4)² = 9, which corresponds to option a).