# Finding the turning point of a relation

I was wondering on how I can find the turning points of this relation:

$$(x^2-7x+5)^2-y^2+7y-5=0$$

The relation is two oval shapes that are seperated. Theres a desmos graph.

https://www.desmos.com/calculator/kfr2po2xxm

Thanks Braiden

• What do you mean by turning points? You mean the "top and bottom" of the two ovals? If yes, then you have to implicitly differentiate this equation to find $\dfrac{dy}{dx}$, and then set it equal to $0$. Then you'll get the coordinates of the $4$ points. – peek-a-boo May 24 at 5:20
• @peek-a-boo how would we do it if wanted to keep it a relation? – Elbraido Gunaratnam May 24 at 6:35