Question

Find the equation of the circle passing through the points (8, 7) and having centre

at (2, −1)​

Answer 1

Step-by-step explanation:

Let the equation of circle be

x^2 + y^2 + 2gx + 2fy + C=0

Given the center is ( 2 , -1 ) i.e g =-2 f=1

then equation is x^2 + y^2 - 4x + 2y + C = 0

Also given a point is passing through the cirlce is

( 8 , 7 )

then , it satisfies ( 8 , 7 )

i.e ( 8 )^2 + ( 7 )^2 - 4( 8 ) + 2( 7 ) + C = 0

64 + 49 - 32 + 14 + C = 0

127 - 32 + C = 0

95 + C = 0

C = -95

therefore , equation of circle is

x^2 + y^2 - 4x + 2y - 95=0