Question

Q1. The ellipse b2x2 + a2y2 =a2b2 is inscribed in a rectangle. Find the length of the
diagonalof the rectangle.​

Answer 1

Answer:

Let 2a be the length of the major axis (rectangle side length) and 2b be the  length of minor axis (rectangle side width)

So if θ is angle between the diagonals of  the rectangle then, tan2θ=ab

⇒tan−11−(ab×ab)ab+ab=tan−122

⇒θ=2tan−1ab=tan−122

⇒tan−11−(ab)2a2b=tan−122

⇒1−(ab)2a2b

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