If $2x^2-3xy-5y^2$ =0 then show that $x^2+y^2\propto xy$ If $ 2x^2 -3xy-5y^2=0$ then show that $$x^2+y^2\propto xy$$ 
This is the question.I tried it to so using elementary algebra but I can't proceed. Somebody please help me.
Thank you
As such, the claim is false.

Counterexample:

$$(-1,1)\to x^2+y^2=2, xy=-1\\
(5,2)\to x^2+y^2=29, xy=10.$$



Anyway, the constraint can be factored as

$$(x+y)(2x-5y)=0$$ so that on both branches of this degenerate hyperbola,

$$(x,mx)\to x^2+y^2=(1+m^2)x^2,xy=mx^2.$$

Then $$x^2+y^2\propto xy.$$
As such, the claim is false.

Counterexample:

$$(-1,1)\to x^2+y^2=2, xy=-1\\
(5,2)\to x^2+y^2=29, xy=10.$$



Anyway, the constraint can be factored as

$$(x+y)(2x-5y)=0$$ so that on both branches of this degenerate hyperbola,

$$(x,mx)\to x^2+y^2=(1+m^2)x^2,xy=mx^2.$$

Then $$x^2+y^2\propto xy.$$