Question

Find the equation of circle whose diameter is the line joining the points $(-4,3)$ and$(12,-1)$. Find also the intercept made by it on y - axis.

Answer 1

The required circle by rule (i)

$(x+4)(x-12)+(y-3)(y+1)=0$

or $x^2+y^2-8x-2y-51=0$

$\therefore g=-4,f=-1,c=-51$

Intercept on y-axis

$2\sqrt{f^2-c}=2\sqrt{(1+51)}=2\sqrt{52}=4\sqrt{13}$