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?

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Answer 1 · 2018-02-22T03:12:56

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

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#