Find the standard form of the equation for the circle with the following properties. Endpoints of a diameter are (-8,7) and (8,3)

Answer 1

Hello Sabrina,

The standard form for a circle is (x - h)² + (y - k)² = r², where the center is (h, k).

The center of the circle will be the midpoint of the points given. That is,

h = (-8 + 8) / 2 = 0 and

k = (7 + 3) / 2 = 5.

Now, the x and y in the equation represent points ON the circle, so you can pick either of the given points. I am going to use (8, 3)

→ (8 - 0)² + (3 - 5)² = r², from which you can solve for r²,

→ 64 + 4 = r²

→ r² = 68

Now just plug in the h, k, and r²

→ (x - 0)² + (y - 5)² = 68

→ x² + (y - 5)² = 68.

Thank you for the question, and have a great day!

Michael E.