MHT CET · Maths · Application of Derivatives
A rectangle of maximum area is inscribed in an ellipse \(\frac{x^2}{25}+\frac{y^2}{16}=1\), then its dimensions are
- A \(4 \sqrt{2}, 6 \sqrt{2}\)
- B \(\sqrt{2}, 5 \sqrt{2}\)
- C \(4 \sqrt{2}, 5 \sqrt{2}\)
- D \(4 \sqrt{2}, \sqrt{2}\)
Answer & Solution
Correct Answer
(C) \(4 \sqrt{2}, 5 \sqrt{2}\)
Step-by-step Solution
Detailed explanation
Length of rectangle \(=10 \cos \theta\) and
breadth of rectangle \(=8 \sin \theta\)
\(\therefore\) Area of rectangle \(=(10 \cos \theta)(8 \sin \theta)=40(\sin \theta)\)
Maximum area will occur when \(\sin 2 \theta=1\)
\(\therefore \sin 2 \theta=\sin \frac{\pi}{2} \quad \Rightarrow \theta=\frac{\pi}{4} \)
\( \therefore P=\left(\frac{5}{\sqrt{2}}, \frac{4}{\sqrt{2}}\right) \Rightarrow \text { Dimensions of rectangle are }\) \(5 \sqrt{2}, 4 \sqrt{2}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The acute angle included between the lines \(x \sin \theta-y \cos \theta=5\) and
\(x \sin \propto-y \cos \propto+11=0\) isMHT CET 2020 Easy - The objective function \(\mathrm{z}=4 \mathrm{z}+5 \mathrm{y}\) subjective to \(2 \mathrm{x}+\mathrm{y} \geq 7\); \(2 x+3 y \leq 15 ; y \leq 3, x \geq 0 ; y \geq 0\) has minimum value at the point.MHT CET 2021 Medium
- The tangent to the circle \(x^2+y^2=5\) at \((1,-2)\) also touches the circle \(x^2+y^2-8 x+6 y+20=0\) then the co-ordinates of the corresponding point of contact isMHT CET 2024 Easy
- If \(\omega\) is a complex cube root of unity and \(A=\left[\begin{array}{cc}\omega & 0 \\ 0 & \omega\end{array}\right]\), then \(A^{-1}=\)MHT CET 2020 Medium
- The degree and order of the differential equation respectively areMHT CET 2016 Easy
- If for for is continuous at and then isMHT CET 2018 Medium
More PYQs from MHT CET
- Which among the following is not a property of alcohols?MHT CET 2022 Easy
- An electric dipole is as shown in figure The electric potential at point \(\mathrm{P}\) due to the dipole is \(\left[\epsilon_0=\right.\) permittivity of free space]
MHT CET 2022 Medium - Find principle of green chemistry to show protection of selective group is not advantageous.MHT CET 2025 Easy
- The distance between the parallel lines \(\frac{x-2}{2}=\frac{y-4}{5}=\frac{z-1}{2}\) and \(\frac{x-1}{3}=\frac{y+1}{5}=\frac{z+3}{2}\) isMHT CET 2021 Medium
- The resistance of a conductivity cell of 0.1 M KCl solution is 120 ohm and conductivity is \(1.64 \times 10^{-4} \mathrm{~S} \mathrm{~cm}^{-1}\). What is the value of cell constant?MHT CET 2024 Easy
- With reference to the principal values, if \(\sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2}\), then \(x^{100}+y^{100}+z^{100}=\)MHT CET 2022 Easy