Question

A diameter of a circle has endpoints P(-10, -2) and Q(4,6).

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.

Answer 1

see below

Explanation:

The center of the circle is 1/2 way between the two endpoints

center = ( (x1+x2)/2, (y1+y2)/2)

center = ( (-10+4)/2, (-2+6)/2)

center = ( (-6)/2, (4)/2)

center = ( -3,2)

The length of the diameter is

d= sqrt( ( y2-y1)^2 + (x2-x1)^2 )

d= sqrt( ( 6 - -2)^2 + (4 - -10)^2 )

d= sqrt( ( 6 +2)^2 + (4 +10)^2 )

d= sqrt( ( 8)^2 + (14)^2 )

d = sqrt(64+196)

d =sqrt(260)

d = sqrt(4*65)

d = 2 sqrt(65)

The radius is 1/2 of the diameter

r = 2 sqrt(65)/2 = sqrt(65)

The equation of a circle is given by

( x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius

( x- -3)^2 + (y-2) ^2 = ( sqrt(65) )^2

( x+3) ^2 + ( y-2) ^2 = 65