What Is the Point C for Maximum Area of Triangle ABC with Ellipse Constraints?

[Government$]

Homework Statement

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?

Homework Equations

Ellipse equations

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.