Question

Equation of the circle which passes through the origin, has its centre on the line $x+y=4$ and cuts the circle $x^2+y^2-4x+2y+4=0$ orthogonally, is

• A. $x^2+y^2-2x-6y=0$
• B. $x^2+y^2-6x-3y=0$
• C. $x^2+y^2-4x-4y=0$
• D. none of these.

Answer 1

The correct option is C $x^2+y^2-4x-4y=0$

Since the centre of the required circle lies on $x+y=4$ let $(g,4-g)$ be this centre,
Since the circle passes through the origin, let
its equation be $x^2+y^2-2gx-2(4-g)y=0$
As this circle cuts
the given circle orthogonally. we have
$2\times g\times 2-2(4-g)=4\Rightarrow 6g=12\Rightarrow g=2$
Hence equation of the
required circle is $x^2+y^2-4x-4y=0$