$\textbf{Find the Ellipse with the largest area such that $\mathbf{x+2y=2}$ is a\\\\ tangent and his foci is at $\mathbf{(-c,0)}$ and $\mathbf{(c,0)}$ for some $\mathbf{0<c<2}$}\\
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1 Answers
11Here 2ae=2c
i.e ae=c...(1)
To find a, refer to the following link:
http://www.targetiit.com/iit-jee-forum/posts/ellipse-19043.html
Thus obtain, a, b in terms of c.
Now, area of ellipse = pi* a* b=f(c) i.e a function of c.
Then, maximise f(c) for 0<c<2.
