AP EAMCET Engineering 18 Sep 2020 Shift 1 Paper

Equation of given ellipse is
x2+4y2=64
⇒‌‌‌

x2

64

+‌

y2

16

=1
Let the vertex P(8‌cos‌θ,4‌sin‌θ) of the rectanglePQRS having greatest area.
∴ Area =A=4(8‌cos‌θ)(4‌sin‌θ)
=64‌sin‌2‌θ
For greatest area sin‌2‌θ=1, so A=64 sq. units and θ=‌

π

4

Therefore point P(4√2,2√2)
So, length of the sides are 8√2 and 4√2.