How do you write an equation of a circle that contains (-2,-2), (2, -2) and (2,2)?

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Answer 1 · 2017-01-05T07:20:39

Equation of circle is #x^2+y^2=8#

Let the equation of the circle be #x^2+y^2+2gx+2fy+c=0#.

As it passes through #(-2,2)#, #(2,-2)# and #(2,2)#, putting their values, we get three equations as follows:

#(-2)^2+2^2+2g(-2)+2fxx2+c=0# or #4+4-4g+4f+c=0#
or #-4g+4f+c=-8# ...................................(1)

#2^2+(-2)^2+2gxx2+2f(-2)+c=0# or #4+4+4g-4f+c=0#
or #4g-4f+c=-8# ...................................(2)

#2^2+2^2+2gxx2+2fxx2+c=0# or #4+4+4g+4f+c=0#
or #4g+4f+c=-8# ...................................(3)

Adding (1) and (2) we get #2c=-16# or #c=-8#.

Subtracting (1) from (3) we get #8g=0# or #g=0#.

and putting these in (1), we get #0+4f-8=-8# i.e. #f=0#

Hence equation is #x^2+y^2-8=0# or #x^2+y^2=8#