JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Consider an elIipse, whose centre is at the origin and its major axis is along the \(x-\) axis. If its eccentricity is \(\frac{3}{5}\) and the distance between its foci is \(6\), then the area (in sq. units) of the quadrilateral inscribed in the ellipse, with the vertices as the vertices of the ellipse, is
- A \(8\)
- B \(32\)
- C \(80\)
- D \(40\)
Answer & Solution
Correct Answer
(D) \(40\)
Step-by-step Solution
Detailed explanation
\(e = 3/5\,\, \&\,\, 2ae = 6 \Rightarrow a = 5\) \(\because \) \({b^2} = {a^2}\left( {1 - {e^2}} \right)\) \( \Rightarrow {b^2} = 25\left( {1 - 9/25} \right)\) \( \Rightarrow b = 4\) \(\therefore \) area of required quadrilateral \( = 4\left( {1/2ab} \right)\) \( = 2ab = 40\)
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 system of equations
\(\begin{aligned}
& x+y+z=6 \\
& x+2 y+5 z=9, \\
& x+5 y+\lambda z=\mu,
\end{aligned}\) has no solution ifJEE Mains 2025 Easy - The lines \(\overrightarrow{ r }=(\hat{ i }-\hat{ j })+\ell(2 \hat{ i }+\hat{ k })\) and \(\overrightarrow{ r }=(2 \hat{ i }-\hat{ j })+ m (\hat{ i }+\hat{ j }-\hat{ k })\)JEE Mains 2020 Hard
- Let \(f, g:(0, \infty) \rightarrow R\) be two functions defined by \(f(x)=\int_{-x}^x\left(|t|-t^2\right) e^{-t^2} d t\) and \(g(x)=\int_0^{x^2} t^{1 / 2} e^{-t} d t\). Then the value of \(\left(\mathrm{f}\left(\sqrt{\log _{\mathrm{e}} 9}\right)+\mathrm{g}\left(\sqrt{\log _{\mathrm{e}} 9}\right)\right)\) isJEE Mains 2024 Hard
- If \(\mathop {\lim }\limits_{x \to 2} \frac{{\tan \left( {x - 2} \right)\{ {x^2} + (k - 2)x - 2k\} }}{{{x^2} - 4x + 4}} = 5\) , then \(k\) is equal toJEE Mains 2014 Hard
- If \(y = {\left[ {x + \sqrt {{x^2} - 1} } \right]^{15}} + {\left[ {x - \sqrt {{x^2} - 1} } \right]^{15}}\) , then \(\left( {{x^2} - 1} \right)\frac{{{d^2}y}}{{d{x^2}}} + x\frac{{dy}}{{dx}}\) is equal toJEE Mains 2017 Hard
- The number of elements in the set \(\left\{A=\left(\begin{array}{ll}a & b \\ 0 & d\end{array}\right): a, b, d \in\{-1,0,1\}\right.\) and \(\left.(I-A)^{3}=I-A^{3}\right\}\) where \(I\) is \(2 \times 2\) identity matrix, is :JEE Mains 2021 Hard
More PYQs from JEE Mains
- Consider the system of linear equations \(-x+y+2 z=0\) \(3 x-a y+5 z=1\) \(2 x-2 y-a z=7\) Let \(S_{1}\) be the set of all \(\mathrm{a} \in {R}\) for which the system is inconsistent and \(S_{2}\) be the set of all \(a \in {R}\) for which the system has infinitely many solutions. If \(n\left(S_{1}\right)\) and \(n\left(S_{2}\right)\) denote the number of elements in \(S_{1}\) and \(\mathrm{S}_{2}\) respectively, thenJEE Mains 2021 Hard
- Let \(\alpha, \beta, \gamma\) be the three roots of the equation \(x ^3+ bx + c =0\). If \(\beta \gamma=1=-\alpha\), then \(b^3+2 c^3-3 \alpha^3-6 \beta^3-8 \gamma^3\) is equal to \(......\).JEE Mains 2023 Hard
- The distance of the point \((1, 0, 2)\) from the point of intersection of the line \(\frac{{x - 2}}{3} = \frac{{y + 1}}{4} = \frac{{z - 2}}{{12}}\) and the plane \(x - y + z = 16\) isJEE Mains 2015 Medium
- A spherical iron ball of radius \(10\,cm\) is coated with a layer of ice of uniform thickness that melts at a rate of \(50\,cm^3/min.\) When the thickness of the ice is \(5\,cm,\) then the rate at which the thickness (in \(cm/min\) ) of ice decreases isJEE Mains 2020 Hard
- An urn contains \(5\) red marbles, \(4\) black marbles and \(3\) white marbles. Then the number of ways in which \(4\) marbles can be drawn so that at the most three of them are red isJEE Mains 2020 Medium
- The term independent of ' \(x\) ' in the expansion of \(\left(\frac{x+1}{x^{2 / 3}-x^{1 / 3}+1}-\frac{x-1}{x-x^{1 / 2}}\right)^{10}\), where \(x \neq 0,1\) is equal to \(.....\)JEE Mains 2021 Hard