Question

The equation of the circle passing through the origin and through the points of intersection of circles $x^2+y^2=4$ and $x^2+y^2-2x-4y+4=0$ is

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

Answer 1

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

The equation of the circle passing through the points of intersection of circles $x^2+y^2=4$ and $x^2+y^2-2x-4y+4=0$ is

$x^2+y^2-4+k(x^2+y^2-2x-4y+4)=0$

But circle passes through origin

So $0+0-4+k(0+0-2\left(0\right)-4\left(0\right)+4)=0$

$\Rightarrow k=1$

Therefore, equation of circle is $x^2+y^2-4+(x^2+y^2-2x-4y+4)=0$

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