Write the standard form the equation for the circle that passes through the points (-9,-16),(-9,32), and (22,15)? then identify the center and radius?

1 Answer
Feb 22, 2018

\text{Center}\ =\ (-2\ ,\ 8)
\text{Radius}=25

Explanation:

To write down the equation of the circle passing through three points, substitute points in the general form of circle and solve coefficients.

x^2+y^2+Dx+Ey+F=0

By putting the given points we get the equations as:

(-9)^2+(-16)^2-9D-16E+F=0

9D+16E-F=337

(-9)^2+(32)^2-9D+32E+F=0

9D-32E-F=1105

(22)^2+(15)^2+22D+15E+F=0

-22D-15E-F=709

By solving the equations using cramer rule, we get:

D=4\ \ \ , \ \ \ E=-16\ \ \ ,\ \ \ F=-557

By putting in the value, we get:

x^2+y^2+4x-16y-557=0

Re-arrange the equation in standard form to get:

=(x-(-2))^2+(y-8)^2=25^2