JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
The length of the minor axis (along \(y-\)axis) of an ellipse in the standard form is \(\frac{4}{\sqrt{3}} .\) If this ellipse touches the line, \(x+6 y=8 ;\) then its eccentricity is
- A \(\sqrt{\frac{5}{6}}\)
- B \(\frac{1}{2} \sqrt{\frac{11}{3}}\)
- C \(\frac{1}{3} \sqrt{\frac{11}{3}}\)
- D \(\frac{1}{2} \sqrt{\frac{5}{3}}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{2} \sqrt{\frac{11}{3}}\)
Step-by-step Solution
Detailed explanation
Let \(\frac{\mathrm{x}^{2}}{\mathrm{a}^{2}}+\frac{\mathrm{y}^{2}}{\mathrm{b}^{2}}=1 ; \mathrm{a}>\mathrm{b}\) \(2 b=\frac{4}{\sqrt{3}} \Rightarrow b=\frac{2}{\sqrt{3}} \Rightarrow b^{2}=\frac{4}{3}\) tangent \(\mathrm{y}=\frac{-\mathrm{x}}{6}+\frac{4}{3}\) compare with…
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
- For real numbers \(a, b (a> b >0)\), let Area \(\left\{(x, y): x^{2}+y^{2} \leq a^{2}\right.\) and \(\left.\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}} \geq 1\right\}=30 \pi\) and Area \(\left\{(x, y): x^{2}+y^{2} \geq b^{2}\right.\) and \(\left.\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}} \leq 1\right\}=18 \pi\) Then the value of \((a-b)^{2}\) is equal toJEE Mains 2022 Medium
- Let a vector \( \overrightarrow{a}=\sqrt{2i}-\hat{j}+\lambda\hat{k}, \lambda>0, \) make an obtuse angle with the vector \( \overrightarrow{b}=-\lambda^{2}\hat{i}+4\sqrt{2j}+4\sqrt{2}\hat{k} \) and an angle \( \theta, \frac{\pi}{6}<\theta<\frac{\pi}{2} \) with the positive z-axis. If the set of all possible values of \( \lambda \) is \( (\alpha,\beta)-\{\gamma\} \), then \( \alpha+\beta+\gamma \) is equal to ___ .JEE Mains 2026 Easy
- Let \([\alpha]\) denote the greatest integer \(\leq \alpha\). Then \([\sqrt{1}]+[\sqrt{2}]+[\sqrt{3}]+\ldots .+[\sqrt{120}]\) is equal to.JEE Mains 2023 Hard
- The sum of all those terms, of the anithmetic progression \(3,8,13, \ldots \ldots .373\), which are not divisible by \(3\),is equal to \(.......\).JEE Mains 2023 Hard
- An angle between the lines whose direction cosines are given by the equations, \(l+ 3m + 5n\, = 0\) and \(5lm -2mn + 6nl = 0\) , isJEE Mains 2018 Hard
- If \(y = y ( x ), x \in\left(0, \frac{\pi}{2}\right)\) be the solution curve of the differential equation \(\left(\sin ^{2} 2 x\right) \frac{d y}{d x}+\left(8 \sin ^{2} 2 x+2 \sin 4 x\right) y=\)\(2 e ^{-4 x }(2 \sin 2 x +\cos 2 x )\), with \(y \left(\frac{\pi}{4}\right)= e ^{-\pi}\), then \(y \left(\frac{\pi}{6}\right)\) is equal to.JEE Mains 2022 Hard
More PYQs from JEE Mains
- If \(\int {\frac{{dx}}{{{{\left( {{x^2} - 2x + 10} \right)}^2}}} = A\left( {{{\tan }^{ - 1}}\left( {\frac{{x - 1}}{3}} \right) + \frac{{f\left( x \right)}}{{{x^2} - 2x + 10}}} \right)} + C\) Where \(C\) is a constant of integration, thenJEE Mains 2019 Hard
- If \(A =\frac{1}{5 ! 6 ! 7 !}\left[\begin{array}{lll}5 ! & 6 ! & 7 ! \\ 6 ! & 7 ! & 8 ! \\ 7 ! & 8 ! & 9 !\end{array}\right]\), then \(|\operatorname{adj}(\operatorname{adj}(2 A ))|\) is equal to:JEE Mains 2023 Hard
- Let a random variable X take values \(0,1,2,3\) with \(\mathrm{P}(\mathrm{X}=0)=\mathrm{P}(\mathrm{X}=1)=\mathrm{p}, \mathrm{P}(\mathrm{X}=2)=\mathrm{P}(\mathrm{X}=3)\) and \(\mathrm{E}\left(\mathrm{X}^2\right)=2 \mathrm{E}(\mathrm{X})\). Then the value of \(8 \mathrm{p}-1\) is :JEE Mains 2025 Easy
- If the system of equations \(x+y+a z=b\) \(2 x+5 y+2 z=6\) \(x+2 y+3 z=3\) has infinitely many solutions, then \(2 a+3 b\) is equal to \(...........\).JEE Mains 2023 Medium
- Among the statements:
I: If \( \begin{vmatrix} 1 & \cos \alpha & \cos \beta \\ \cos \alpha & 1 & \cos \gamma \\ \cos \beta & \cos \gamma & 1 \end{vmatrix} = \begin{vmatrix} 0 & \cos \alpha & \cos \beta \\ \cos \alpha & 0 & \cos \gamma \\ \cos \beta & \cos \gamma & 0 \end{vmatrix} \), then \( \cos^{2}\alpha+\cos^{2}\beta+\cos^{2}\gamma=\frac{3}{2} \)
II: If \( \begin{vmatrix} x^{2}+x & x+1 & x-2 \\ 2x^{2}+3x-1 & 3x & 3x-3 \\ x^{2}+2x+3 & 2x-1 & 2x-1 \end{vmatrix} = px+q \), then \( p^{2}=196q^{2} \),JEE Mains 2026 Easy - Let a variable line of slope \(m>0\) passing through the point \((4,-9)\) intersect the coordinate axes at the points \(A\) and \(B\). the minimum value of the sum of the distances of \(\mathrm{A}\) and \(\mathrm{B}\) from the origin isJEE Mains 2024 Hard