Here's the question- Find the maximum area of an isosceles triangle inscribed in the ellipse $x^2/a^2 + y^2/b^2 = 1$. My teacher solved it by considering two arbitrary points on the ellipse to be vertices of the triangle, being $(a\cos\theta, b\sin \theta)$ and $(a\cos\theta, -b\sin \theta)$. (Let's just say $\theta$ is theta) and then proceeded with the derivative tests(which i understood) But, he didn't indicate what our $\theta$ was,and declared that these points always lie on an ellipse. Why so? And even if they do, what's the guarantee that points of such a form will be our required vertices? One more thing, I'd appreciate it if you could suggest another way of solving this problem. Thank you!
An easy Calculus Problem
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calculus
derivatives