Question

Equation of the circle passing through the point $(1,1)$ and point of intersection of circles $x^2+y^2=6$ and $x^2+y^2-6x+8=0$ is

• A. $x^2+y^2-6x+4=0$
• B. $x^2+y^2-3x+1=0$
• C. $x^2+y^2-4y+2=0$
• D. $x^2+y^2-3y+1=0$

Answer 1

The correct option is B $x^2+y^2-3x+1=0$

Family of circles passing through the points of intersection of the two circles $x^2+y^2-6=0$ and $x^2+y^2-6x+8=0$ is
$(x^2+y^2-6)+\lambda (x^2+y^2-6x+8)=0$
As required circle passes through $(1,1),$ then
$(1+1-6)+\lambda (1+1-6+8)=0$
$\Rightarrow \lambda =1$
$\therefore$ The required circle eqation is
$2x^2+2y^2-6x+2=0$
$\Rightarrow x^2+y^2-3x+1=0$