A diameter of a circle has endpoints P(-10,-2) and Q(4,
A. Find the center of the circle
B. Find the radius. If your answer is not an integer,express it in radical form
C. Write an equation for the circle
A. To find the center of the circle, we need to find the midpoint of the diameter PQ. We use the midpoint formula:
Midpoint = ( (x1 + x2)/2 , (y1 + y2)/2)
Midpoint = ( (-10 + 4)/2 , (-2 + 9)/2)
Midpoint = ( -3 , 3.5)
Therefore, the center of the circle is (-3, 3.5).
B. To find the radius of the circle, we need to find the distance between the center and one of the endpoints of the diameter, say P. We use the distance formula:
Distance = sqrt( (x2 - x1)^2 + (y2 - y1)^2 )
Distance = sqrt( (-10 - (-3))^2 + (-2 - 3.5)^2 )
Distance = sqrt( 49 + 31.25 )
Distance = sqrt( 80.25 )
Therefore, the radius of the circle is sqrt(80.25) or approximately 8.96.
C. The equation for a circle with center (h,k) and radius r is:
(x - h)^2 + (y - k)^2 = r^2
Using the center and radius we found in parts A and B, we have:
(x - (-3))^2 + (y - 3.5)^2 = (8.96)^2
Simplifying and expanding, we get:
(x + 3)^2 + (y - 3.5)^2 = 80.25
Therefore, the equation for the circle is (x + 3)^2 + (y - 3.5)^2 = 80.25.