Find the equation of the circle with center on the yaxis and

Find the equation of the circle with center on the y-axis and has y-intercepts at 2 and -8.

Solution

The equation of a circle with center at (a, b) and radius r is
(x-a)2+(y-b)2=r2

So we just need the center and the radius. We know the x-coordinate of the center is 0 because it is on the y axis. We know it is halfway between the y-intercepts. So the center is (0, -3). The radius is the distance from the center to a point on the circle. It is convenient in this case to use a y-intercept. We find the radius to be |-3-2|=5. a = 0, b = -3, r = 5

We get
x2+(y+3)2=25