Question

Equation of smallest circle passing through points of intersection of line $x+y=1$ & circle $x^2+y^2=9$ is

• A. $x^2+y^2+x+y-8=0$
• B. $x^2+y^2-x-y-8=0$
  
• C. $x^2+y^2-x+y-8=0$
• D. $x^2+y^2+x+y+8=0$

Answer 1

The correct option is B

$x^2+y^2-x-y-8=0$

Let the circle be $(x^2+y^2-9)+\lambda (x+y-1)=0$

Centre of this circle is $(-\frac{\lambda }{2},-\frac{\lambda }{2})$

For the circle to be smallest, this centre must lie on the line, $x+y-1=0$

$\Rightarrow \lambda =-1$

$\Rightarrow$ The circle is $x^2+y^2-x-y-8=0$