Ellipse and triangle problem

Government$

1. The problem statement, all variables and given/known data
Points are A(-6,2) and B(-3,4) and ellipse 4x^2 + 9y^2 = 72. Point C(x,y) for which triangle ABC has largest area is?


2. Relevant equations
Ellipse equations


3. The attempt at a solution
I don't know even where to start. As far as i am concerned that point can be any number as long as i can construct triangle using that point.

Villyer

I'm assuming that point C has to on the ellipse.

They give you a side of the triangle, AB, and you need to find a third point on the ellipse that maximizes the area.

I can think of a few methods that do this, what level math are you taking?

Government$

Thank you for the hint i solved the problem. I am currently reviewing pre calclus so i could move forward.