The question here is to solve $x^2p+y^2q+z^2=0$ passing through a given curve $\Gamma : xy=x+y,z=1$
I am trying to solve it by Lagrange's method, where $\frac{dx}{x^2}=\frac{dy}{y^2}$, thus I get $1/y-1/x =c$ and then I substituted $x+y$ in place of $xy$ in denominator.
Thus I found: $(x-y)/(x+y)=c$
Is it correct ?
Soham