WBJEE · Maths · Ellipse
S and \(T\) are the foci of an ellipse and B is end point of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is
- A \(\frac{1}{4}\)
- B \(\frac{1}{3}\)
- C \(\frac{1}{2}\)
- D \(\frac{2}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
Hints : \(\frac{\mathrm{b}}{\mathrm{ae}}=\sqrt{3} ; \quad \mathrm{b}=\sqrt{3} \mathrm{ae}\) \[ \mathrm{e}^2=\frac{\mathrm{a}^2-3 \mathrm{a}^2 \mathrm{e}^2}{\mathrm{a}^2}=1-3 \mathrm{e}^2 ; \quad 4 \mathrm{e}^2=1 \Rightarrow \mathrm{e}=\frac{1}{2} \]
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
- In a triangle \(\mathrm{PQR}, \angle \mathrm{R}=\pi / 2\). If \(\tan \left(\frac{\mathrm{p}}{2}\right)\) and \(\tan \left(\frac{\mathrm{Q}}{2}\right)\) are roots of \(\mathrm{ax}^2+\mathrm{bx}+\mathrm{c}=0\), where \(\mathrm{a} \neq 0\), then which one is true ?WBJEE 2010 Medium
- Let \(\Gamma\) be the curve \(y=b e^{-x / a} \& L\) be the straight line \(\frac{x}{a}+\frac{y}{b}=1\) where \(a, b \in \mathbb{R}\)WBJEE 2024 Easy
- Let \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) be real numbers, each greater than 1 , such that \(\frac{2}{3} \log _{\mathrm{b}} \mathrm{a}+\frac{3}{5} \log _{\mathrm{c}} \mathrm{b}+\frac{5}{2} \log _{\mathrm{a}} \mathrm{c}=3\). If the value of \(b\) is 9 , then the value of ' \(a\) ' must beWBJEE 2021 Easy
- Let the tangent and normal at any point \(P\left(at^2\right.\), 2at), \((a > 0)\), on the parabola \(y^2=4 a x\) meet the axis of the parabola at \(T\) and \(\mathrm{G}\) respectively. Then the radius of the circle through \(\mathrm{P}, \mathrm{T}\) and \(\mathrm{G}\) isWBJEE 2022 Medium
- \(P\) is the extremity of the latusrectum of ellipse \(3 x^{2}+4 y^{2}=48\) in the first quadrant. The eccentric angle of \(P\) isWBJEE 2019 Easy
- If \(x\) satisfies the inequality \(\log _{25} x^2+\left(\log _5 x\right)^2 < 2\), then \(x\) belongs toWBJEE 2022 Easy
More PYQs from WBJEE
- Eleven equal point charges, all of them having a charge \(+Q\), are placed at all the hour positions of a circular clock of radius \(r\). except at the \(10 \mathrm{h}\) position. What is the clectric field strength at the centre of the clock?WBJEE 2019 Medium
- The mean and variance of a binomial distribution are 4 and 2 respectively. Then the probability of exactly two succsses isWBJEE 2021 Medium
- In triangle \(\mathrm{ABC}, \mathrm{a}=2, \mathrm{~b}=3\) and \(\sin \mathrm{A}=\frac{2}{3}\), then \(\mathrm{B}\) is equal toWBJEE 2009 Easy
- If \(y=e^{m \sin ^{-1} x}\) then \(\left(1-x^{2}\right) \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}-k y=0,\) where \(k\) is
equal toWBJEE 2017 Medium - The number of points at which the function \(f(x)=\max \{a-x, a+x, b\},-\infty < x < \infty\) \(0 < a < b\) cannot be differentiable, isWBJEE 2016 Medium
- A point source is placed at coordinates (0,1) in \(x y\) -plane. A ray of light from the source is reflected on a plane mirror placed along the
\(X\) -axis and perpendicular to the \(x y\) -plane. The reflected ray passes through the point \((3,3) .\) What is the path length of the ray from (0,1) to (3,3)\(?\)WBJEE 2018 Easy