Question

if x+y=3 is the equation of the chord AB of the circle
${x}^{2} + {y }^{2} - 2x + 4y - 8 = 0$
find the equation of the circle having AB as diameter

Answer 1

Let A(x1,y1) and B(x2,y2)

Eqn of circle is (x – x1)(x – x2) + (y – y1)(y – y2) = 0

x2 – (x1 + x2)x +x1x2 + y2 – (y1 + y2)y +y1y2 = 0

x2 – (-2)x + (-a2)+ y2 – (-4)y +(-b2) = 0

x2 + 2x – a2+ y2 + 4y – b2 = 0

x2 + y2 + 2x + 4y – a2  – b2 = 0

is required eqn


Hope This Helps :)