Question

Equation of the circle which passes through the intersection of $x^2+y^2+13x-3y=0$ and $2x^2+2y^2+4x-7y-25=0$ whose centre lies on $13x+30y=0$ is

• A. $x^2+y^2+5x+y=0$
• B. $4x^2+4y^2+30x-13y-25=0$
• C. $2x^2+2y^2+3x-4y=0$
• D. $4x^2+4y^2-8x+7y+10=0$

Answer 1

Answer: (B)

The equation of required circle is $s_1+\lambda s_2=0$
$=x^2(1+\lambda )+y^2(1+\lambda )+x(2+13\lambda )-y$
$\left(\frac{7}{2}+3\lambda \right)-\frac{25}{2}=0$
Centre $=\left(\frac{-(2+13\lambda )}{2},\frac{7/2+3\lambda }{2}\right)$
$\because$ Centre lies on $13x+30y=0$
$\Rightarrow -13\left(\frac{2+13\lambda }{2}\right)+30\left(\frac{7/2+3\lambda }{2}\right)=0$
$\Rightarrow \lambda =1$