AP EAMCET · Maths · Ellipse

If \(l\) and \(b\) are respectively the length and breadth of the rectangle of greatest area that can be inscribed in the ellipse \(x^2+4 y^2=64\), then \((l, b)=\)

A \((16 \sqrt{2}, 4 \sqrt{2})\)
B \((8 \sqrt{2}, 6 \sqrt{2})\)
C \((8 \sqrt{2}, 4 \sqrt{2})\)
D \((6 \sqrt{2}, 4 \sqrt{2})\)

Verified Solution

Answer & Solution

Correct Answer

(C) \((8 \sqrt{2}, 4 \sqrt{2})\)

Step-by-step Solution

Detailed explanation

Let \(P Q R S\) be a rectangle inscribed in the ellipse \(\frac{x^2}{64}+\frac{y^2}{16}=1\). Let the coordinate of \(P\) be \((8 \cos \theta, 4 \sin \theta)\). Then, the coordinates of \(Q, R\) and \(S\) are \((-8 \cos \theta, 4 \sin \theta),(-8 \cos \theta, 4 \sin \theta)\) and…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From AP EAMCET

Explore more questions on app

(A)	Isothermal process	(i)	$q = ∆ U$
(B)	Adiabatic process	(ii)	$W = - P \times ΔV$
(C)	Isobaric process	(iii)	$W = ∆ U$
(D)	Isochoric process	(iv)	$W = - nRTln (\frac{V_{f}}{V_{i}})$