AP EAMCET · Maths · Ellipse
If the angle between the straight lines joining the foci and the ends of the minor axis of the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) is \(90^{\circ}\), then it eccentricity is
- A \(1 / 2\)
- B \(1 / 4\)
- C \(1 / 3\)
- D \(1 / \sqrt{2}\)
Answer & Solution
Correct Answer
(D) \(1 / \sqrt{2}\)
Step-by-step Solution
Detailed explanation
Apply pythagoras theorem, in \(\Delta A S_1 S_2\) \(\left(S_1 A\right)^2+\left(A S_2\right)^2=\left(S_1 S_2\right)^2\) \(a^2+a^2=(2 a e)^2\) \(\Rightarrow \quad 2 a^2=4 a^2 e^2\) \(\therefore \quad e=\frac{1}{\sqrt{2}}\)
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
- If \(m\) and \(M\) respectively denote the minimum and maximum of \(f(x)=(x-1)^2+3\) for \(x \in[-3,1]\), then the ordered pair \((m, M)\) is equal toAP EAMCET 2008 Easy
- A particle moves along the curve \(y=x^2+2 x\). Then, the point on the curve such that \(x\) and \(y\) coordinates of the particle change with the same rate isAP EAMCET 2004 Easy
- AP EAMCET 2022 Medium
- \[
\int \frac{1}{\cos 4 x \cos 2 x} d x=\frac{1}{2 \sqrt{2}} \log \left(\frac{1+f(x)}{1-f(x)}\right)
\]
\(-\frac{1}{2} \log g(x)+C\), then \(g\left(\frac{\pi}{6}\right)-\sqrt{2} f\left(\frac{\pi}{6}\right)=\)AP EAMCET 2022 Hard - \(\frac{1}{2 !}+\frac{1+2}{3 !}+\frac{1+2+3}{4 !}+\ldots\) is equal to :AP EAMCET 2003 Medium
- If \(k\) is one of the roots of the equation \(x^2-25 x+24=0\) such that \(A=\left[\begin{array}{lll}1 & 2 & 1 \\ 3 & 2 & 3 \\ 1 & 1 & k\end{array}\right]\) is a non-singular matrix, then \(A^{-1}=\)AP EAMCET 2019 Easy
More PYQs from AP EAMCET
- The energy dissipated per unit volume per cycle in the hysteresis of an iron sample of mass \(10 \mathrm{~kg}\) is \(200 \mathrm{Jm}^{-3} \mathrm{cycle}^{-1}\). The density of iron is \(7500 \mathrm{~kg} \mathrm{~m}^{-3}\). The loss of energy per hour at 50 cycle s \(^{-1}\) isAP EAMCET 2017 Hard
- The perimeter of the locus of the point \(P\) which divides the line segment \(\overrightarrow{Q A}\) internally in the ratio \(1: 2\), where \(A=(4,4)\) and \(Q\) lies on the circle \(x^2+y^2=9\) isAP EAMCET 2024 Easy
- The correct order of increasing acidic strength among the following isAP EAMCET 2020 Medium
- The equation of circle with centre \((2,-3)\) and touching \(X\)-axis isAP EAMCET 2022 Easy
- The mean and the standard deviation of a data of 8 items are 25 and 5 respectively. If two items 15 and 25 are added to this data, then the variance of the new data isAP EAMCET 2018 Medium
- If \(\alpha, \beta, \gamma\) are the roots of \(x^3+2 x+5=0\), then \(\sum \frac{\beta+\gamma}{\alpha^2}=\)AP EAMCET 2023 Medium