Question

A circle has center (5, 4) and radius 8. Which gives the equation for the circle?

A. (x + 5)² + (y - 4)² = 8
B. (x - 5)² + (y + 4)² = 8
C. (x + 5)² + (-4)² = 64
D. (x - 5)² + (y + 4)² = 64

Answer 1

The equation for the circle with center (5, 4) and radius 8 is (x - 5)² + (y - 4)² = 64.

Step-by-step explanation:

The equation for a circle with center (h, k) and radius r is given by:

(x - h)² + (y - k)² = r²

In this case, the center is (5, 4) and the radius is 8. Substituting these values into the equation, we get:

(x - 5)² + (y - 4)² = 8²

Therefore, the correct equation for the circle is (x - 5)² + (y - 4)² = 64 (Option D).