For the function $$ f(x,y)=y\sqrt{2x^2+4y^2+18}-x$$ Find the domain of $c$ such that the equation $$f(x,y)=c$$ is an ellipse.
I tried it two times in desmos while taking $c$ as slider and I found no value of c gives ellipse shape. I think the question is wrong. What you have to say about this ?
I tried analytically also by squaring both sides but I'm getting $y^4$ which is not allowing me to convert that equation in generalised ellipse shape. Thanks