A (-2,5), B(2,-3), C(2,7) are the three points on a circle.?

Question

i). Find the equations of the perpendicular bisectors of AB and BC.

ii). Find the coordinates of the point at which these two perpendicular bisectors meet

iii). Hence find the equation of the cicle through A, B, C.

PLS HELP.

Answer 1

A (-2,5), B(2,-3), C(2,7) are the three points on a circle.?

i). Find the equations of the perpendicular bisectors of AB and BC.

slope of AB is -2 so the slope of the perpendicular bisector is 1/2 and the  equation will be

y-5=1/2(x+2)

2y-10=x+2

x-2y=-12

slope of BC is undefined so its equation is x=2 and the equation of its perpendicular bisector is y=2 because the midpoint is (2,2)

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ii). Find the coordinates of the point at which these two perpendicular bisectors meet

(-8,2)

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iii). Hence find the equation of the cicle through A, B, C.