Write the equation of the circle with a diameter whose endpoints are (0,7) and (0,3)
The first thing you need is the equation of a circle:
(x-h)2 + (y-k)2 = r2
Where (h,k) are the coordinates of the center of the circle and r is its radius. So we need to find h, k and r. The points (7,7) and (0,3) lie on the circle and the line between them is a diameter, so it passes through the center (h,k). The mid-point between (0,7) and (0,3) is where the center is.
To find (h,k), there is a formula to find the midpoint on a line connecting two points:
Midpoint = (h,k) = ( (x1+x2)/2, (y1+y2)/2 ) =( (0+0)/2, (7+3)/2 ) = (0,5)
Hence the center is located at (h,k) = (0,5)
Now we need to find the distance from either point (0,7) or (0,3) to (h,k) to determine the circle's radius. There's a formula for that as well:
distance2 = (x2-x1)2 + (y2-y1)2
Picking (h,k)=(0,5) and (0,3)
d2 = r2 = (0-0)2 + (5-3)2 = 4
So the equation of the circle is:
(x)2 + (y-5)2 = 4
