Question

Two circles $x^2+y^2=6$ and $x^2+y^2-6x+8=0$ are given. Then the equation of the circle through their point of intersection and the point $(1,1)$ 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. $noneofthese$

Answer 1

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

$C_1:x^2+y^2=6$

$C_2:x^2+y^2-6x+8=0$

$C_3:(x^2+y^2-6)+\lambda (x^2+y^2-6x+8)=0$

Since $C_3$ passes through $(1,1)$

$-4+\lambda \left(4\right)=0$

$\Rightarrow \lambda =1$

$\therefore C_3:2x^2+2y^2-6x+2=0$

$\Rightarrow x^2+y^2-3x+1=0$