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

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To find point C for maximum area of triangle ABC with given points A(-6,2) and B(-3,4) constrained by the ellipse 4x^2 + 9y^2 = 72, point C must lie on the ellipse. The area of triangle ABC can be maximized by determining the optimal position of point C along the ellipse's boundary. Various mathematical methods can be employed to solve this problem, including calculus and geometric principles. The discussion highlights the importance of understanding the relationship between the triangle's area and the ellipse's constraints. Ultimately, the problem was resolved after considering hints and reviewing relevant mathematical concepts.
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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.
 
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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?
 
Thank you for the hint i solved the problem. I am currently reviewing pre calclus so i could move forward.
 

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