What is the standard equation of circle with a diameter whose endpoints are (5, -17) and (5,1)?

Answer 1

Since the endpoints are (5,-17) and (5,1) we can find the diameter of the circle by finding the distance between the endpoints. In this case the diameter would be 1-(-17) = 18. The radius = 1/2 the diameter, so the radius is 18/2 = 9.

The center point would be the point half way between the two endpoints, or one radius away from each endpoint. Since the radius is 9, and the endpoints are (5,-17) and (5,1), the center would be at point (5,-8).

The standard equation for a circle is (x-h)² + (y-k)² = r², where h and k are the x and y coordinates of the center of the circle. Since r = 9 and the center is at (5,-8), the equation is

(x-5)² + (y-(-8))² = 9²

(x-5)² + (y+8)² = 81

We can verify this by substituting one of the endpoints for x and y in the equation. If we use (5,1)

(5-5)² + (1+8)² = 81

0 + 9² = 81

81 = 81

So that checks out