Question

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

Answer 1

It is given that the end points of the diameter of the circle are (-4, 3) and (12, -1).
Required equation of circle $(x+4)(x-12)+(y-3)(y+1)$
or $x^2+y^2-8x-2y—-51=0\dots \left(i\right)$
Putting x = 0 in (i)
$y^2-2y-51=0\Rightarrow y^2-2y-51=0\Rightarrow y=1+2\sqrt{13}$
Hence, the intercepts made by it on the
y-axis is $1+2\sqrt{13}-1+2\sqrt{13}=4\sqrt{13}$