Question

Write the equation of the circle that has a diameter with endpoints (3,7)
and (3, 1)

Answer 1

(x - 3)^2 + (y - 4)^2 = 3^2

Explanation:

Notice that both endpoints are on the vertical line x = 3. Thus, to determine the diameter of this circle, we need only subtract 1 from 7, obtaining 6. The diameter is 6, so the radius is 3.

The center is on the vertical line x = 3 and is halfway between the endpoints of the diameter, that is, at y = 4. (3, 4) describes this point.

Then we insert the known quantities into the general equation for a circle with center at (h, k) and radius r: 3 for h, 4 for k and 3 for r:

(x - 3)^2 + (y - 4)^2 = 3^2 is the desired equation.