JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is \(10\) and one of the foci is at \((0, 5\sqrt 3 )\), then the length of its latus rectum is
- A \(6\)
- B \(5\)
- C \(8\)
- D \(10\)
Answer & Solution
Correct Answer
(B) \(5\)
Step-by-step Solution
Detailed explanation
\(be = 5\sqrt 3 \) \({b^2}{e^2} = 75\) \(\left( {b - a} \right)\left( {b + a} \right) = 75 \Rightarrow b + a = 15\) \( \Rightarrow b = 10,a = 5\) \(LR = \frac{{2{a^2}}}{b}5\)
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
- An angle of intersection of the curves, \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) and \(\mathrm{x}^{2}+\mathrm{y}^{2}=\mathrm{ab}, \mathrm{a}>\mathrm{b}\), is :JEE Mains 2021 Hard
- If \(B = \left[ {\begin{array}{*{20}{c}}
5&{2\alpha }&1\\
0&2&1\\
\alpha &3&{ - 1}
\end{array}} \right]\) is the inverse of a \(3 \times 3\) matrix \(A\), then the sum of all values of \(\alpha \) for which \(det\, (A) + 1 = 0\), isJEE Mains 2019 Hard - The value of \(r\) for which \(^{20}{C_r}^{20}{C_0}{ + ^{20}}{C_{r - 1}}^{20}{C_1}{ + ^{20}}{C_{r - 2}}^{20}{C_2} + ...{ + ^{20}}{C_0}^{20}{C_r}\) is maximum isJEE Mains 2019 Hard
- The square of the distance of the point of intersection of the line \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z+1}{6}\) and the plane \(2 x-y+z=6\) from the point \((-1,-1,2)\) is .... .JEE Mains 2021 Medium
- Let \(f : R \to R\) be a function such that \(f(2 - x)\, = f(2 + x)\) and \(f(4 -x)\, = f(4 + x)\), for all \(x \in R\) and \(\int\limits_0^2 {f\left( x \right)\,dx = 5} \) . Then the value of \(\int\limits_{10}^{50} {f\left( x \right)\,\,dx} \) isJEE Mains 2015 Hard
- \(A\) particle is moving in the \(x y\)-plane along a curve \(C\) passing through the point \((3,3)\). The tangent to the curve \(C\) at the point \(P\) meets the \(x\)-axis at \(Q\). If the \(y\)-axis bisects the segment \(P Q\), then \(C\) is a parabola withJEE Mains 2022 Hard
More PYQs from JEE Mains
- Let \(X=\{11,12,13, \ldots ., 40,41\}\) and \(Y=\{61,62\), \(63, \ldots ., 90,91\}\) be the two sets of observations. If \(\bar{x}\) and \(\bar{y}\) are their respective means and \(\sigma^2\) is the variance of all the observations in \(X \cup Y\), then \(\left|\overline{ x }+\overline{ y }-\sigma^2\right|\) is equal to \(.................\).JEE Mains 2023 Hard
- If \(A\) is a symmetric matrix and \(B\) is a skew-symmetrix matrix such that \(A + B = \left[ {\begin{array}{*{20}{c}}
2&3\\
5&{ - 1}
\end{array}} \right]\) , then \(AB\) is equal toJEE Mains 2019 Hard - Let \(S=\left[-\pi, \frac{\pi}{2}\right)-\left\{-\frac{\pi}{2},-\frac{\pi}{4},-\frac{3 \pi}{4}, \frac{\pi}{4}\right\}\). Then the number of elements in the set \(=\{\theta \in S : \tan \theta(1+\sqrt{5} \tan (2 \theta))=\sqrt{5}-\tan (2 \theta)\}\) is \(...\)JEE Mains 2022 Hard
- Let \(\vec{a}=3 \hat{i}+\hat{j}-2 \hat{k}, \vec{b}=4 \hat{i}+\hat{j}+7 \hat{k}\) and \(\overrightarrow{\mathrm{c}}=\hat{\mathrm{i}}-3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}\) be three vectors. If a vectors \(\overrightarrow{\mathrm{p}}\) satisfies \(\overrightarrow{\mathrm{p}} \times \overrightarrow{\mathrm{b}}=\overrightarrow{\mathrm{c}} \times \overrightarrow{\mathrm{b}}\) and \(\overrightarrow{\mathrm{p}} \cdot \overrightarrow{\mathrm{a}}=0\), then \(\overrightarrow{\mathrm{p}} \cdot(\hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}})\) is equal toJEE Mains 2024 Hard
- Let \(\vec{a}\) and \(\vec{b}\) be two vectors such that \(|\vec{a}|=1,|\vec{b}|=4\) and \(\vec{a} \cdot \vec{b}=2\). If \(\vec{c}=(2 \vec{a} \times \vec{b})-3 \vec{b}\) and the angle between \(\vec{b}\) and \(\vec{c}\) is \(\alpha\), then \(192 \sin ^2 \alpha\) is equal toJEE Mains 2024 Medium
- Let \(\quad S=109+\frac{108}{5}+\frac{107}{5^2}+\ldots \ldots . .+\frac{2}{5^{107}}+\frac{1}{5^{108}}\). Then the value of \(\left(16 S -(25)^{-34}\right)\) is equal to \(............\).JEE Mains 2023 Hard