COMEDK · Maths · 14. Ellipse
If the distance between the foci is equal to the length of the latus rectum, then the eccentricity of the ellipse is
- A \(\dfrac{1 \pm \sqrt{5}}{2}\)
- B \(\dfrac{1-\sqrt{5}}{2}\)
- C \(\dfrac{\sqrt{5}+1}{2}\)
- D \(\dfrac{\sqrt{5}-1}{2}\)
Answer & Solution
Correct Answer
(D) \(\dfrac{\sqrt{5}-1}{2}\)
Step-by-step Solution
Detailed explanation
For an ellipse with semi-major axis \(a\) and semi-minor axis \(b\), the distance between the foci is \(2ae\) and the length of the latus rectum is \(\dfrac{2b^2}{a}\). Given that the distance between the foci is equal to the length of the latus rectum, we have…
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
- \(\text { The area of the region enclosed by the curve }\left\{(x, y): 4 x^2+25 y^2=100\right\} \text { is }\)COMEDK 2024 Easy
- The value of \(1 \cdot 1 !+2 \cdot 2 !+3 \cdot 3 !+\quad+n \cdot n !\) isCOMEDK 2021 Medium
- The value of \(\frac{1}{1 \cdot 4}+\frac{1}{4 \cdot 7}+\frac{1}{7 \cdot 10}+\ldots+\frac{1}{(3 n-2)(3 n+1)}\) isCOMEDK 2024 Hard
- If \(f(x)+2 f(1-x)=x \forall x \in R\), then \(f(x)\) is equal toCOMEDK 2024 Medium
- \(\text { The value of } \dfrac{i^{1004}+i^{1006}+i^{1008}+i^{1010}+i^{1012}}{i^{510}+i^{508}+i^{506}+i^{504}+i^{502}} \text { is }\)COMEDK 2024 Easy
- If \(A=\left[\begin{array}{cc}k+1 & 2 \\ 4 & k-1\end{array}\right]\) is a singular matrix, then possible values of \(\mathrm{k}\) areCOMEDK 2023 Easy
More PYQs from COMEDK
- The inductance in a coil plays the same role asCOMEDK 2014 Easy
- \(\text { If } \operatorname{cosec}(90+A)+x \cos A \cot (90+A)=\sin (90+A) \text { then the value of } x \text { is }\)COMEDK 2023 Easy
- If two lines \(L_1: \frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}\) and \(L_2: \frac{x-3}{1}=\frac{y-k}{2}=z\) intersect at a point, then \(2 k\) is equal toCOMEDK 2023 Medium
- The number of gram molecules of chlorine in \(6.02 \times 10^{25}\) hydrogen chloride molecules isCOMEDK 2020 Easy
- The total number of terms in the expansion of \((x+y)^{60}+(x-y)^{60}\) isCOMEDK 2023 Medium
- Kinetic energy of one mole of an ideal gas at \(300 \mathrm{~K}\) in \(\mathrm{kJ}\) isCOMEDK 2013 Easy