Question

Locus of mid point of chords of $x^2+y^2+2gx+2fy+c=0$ that pass through the origin, is

• A. $x^2+y^2+2gx+2fy+c=0$
• B. $x^2+y^2+gx+fy+c=0$
• C. $x^2+y^2+gx+fy=0$
• D. $2(x^2+y^2+gx+fy)+c=0$

Answer 1

The correct option is C $x^2+y^2+gx+fy=0$

Let the mid point of chords of circle be $P(h,k).$
Equation of this chord is $T=S_1$
$xh+yk+g(x+h)+f(y+k)+c=h^2+k^2+2gh+2fk+c.$
It passes through $(0,0)$
$\Rightarrow h^2+k^2+gh+fk=0$
Hence required locus is $x^2+y^2+gx+fy=0$