Question

The equation of the circle which passes through the point of intersection of circles $x^2+y^2-8x-2y+7=0$ and $x^2+y^2-4x+10y+8=0$ and having its centre on $y-$axis, will be

• A. $x^2+y^2+22y+9=0$
• B. $x^2+y^2+22x-9=0$
• C. $x^2+y^2+22x+9=0$
• D. $x^2+y^2+22y-9=0$

Answer 1

The correct option is A $x^2+y^2+22y+9=0$

Let $S_1$ be $x^2+y^2-8x-2y+7=0$ & $S_2$ be $x^2+y^2-4x+10y+8=0$

Then, equation of circle through points of intersection of $S_1,S_2$ is

$S_1+K(S_2-S_1)=0$

$\Rightarrow (x^2+y^2-8x-2y+7)+K(4x+12y+1)=0$

$x^2+y^2+(4K-8)x+y(12K-2)+7+K=0$ ___ (1)

As circle has centre on y-axis $\Rightarrow -\left(\frac{4K-8}{2}\right)=0$ [abscissa = $\frac{-9}{2}=0]$

$\Rightarrow K=2$

Substituting in (1)

$x^2+y^2+22y+9=0$ is the required equation

$\therefore$ Option A is correct