If this condition is satisfied, show that the equation of the locus of the foot of the perpendicular from the origin to the line \(\displaystyle px+qy+r=0\) is

\(\displaystyle (a+b)(x^2+y^2)+2gx+2fy+c=0\)

I've done the first part. The answers I found are:

\(\displaystyle x^2(ar^2-2gpr+p^2c)+2xy(hr^2-fpr-gqr+pqc)+y^2(br^2-2fqr+q^2c)=0\)

and

\(\displaystyle r^2(a+b)-2r(gp+fq)+c(p^2+q^2)=0\)

How do I proceed with the next part?

Thanks!