KCET · Maths · Mathematical Reasoning
The eccentricity of the ellipse \( \frac{x^{2}}{36}+\frac{y^{2}}{16}=1 \) is
- A \( \frac{2 \sqrt{5}}{6} \)
- B \( \frac{2 \sqrt{5}}{4} \)
- C \( \frac{2 \sqrt{13}}{6} \)
- D \( \frac{2 \sqrt{13}}{4} \)
Answer & Solution
Correct Answer
(A) \( \frac{2 \sqrt{5}}{6} \)
Step-by-step Solution
Detailed explanation
Given equation of ellipse,
\[
\frac{x^{2}}{36}+\frac{y^{2}}{16}=1
\]
We know that eccentricity is given by,
\[
e=\sqrt{\frac{a^{2}-b^{2}}{a^{2}}}
\]
\[
\begin{array}{l}
\text { Here } a^{2}=36 \text { and } b^{2}=16 \\
\text { So, } e=\sqrt{\frac{36-16}{36}}=\frac{2 \sqrt{5}}{6}
\end{array}
\]
\[
\frac{x^{2}}{36}+\frac{y^{2}}{16}=1
\]
We know that eccentricity is given by,
\[
e=\sqrt{\frac{a^{2}-b^{2}}{a^{2}}}
\]
\[
\begin{array}{l}
\text { Here } a^{2}=36 \text { and } b^{2}=16 \\
\text { So, } e=\sqrt{\frac{36-16}{36}}=\frac{2 \sqrt{5}}{6}
\end{array}
\]
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 the function \(f(x)=\left\{\begin{array}{cl}\frac{1-\cos x}{x^{2}}, & \text { for } x \neq 0 \\ k, & \text { for } x=0\end{array}\right.\) continuous at \(x=0\), then the value of \(k\) isKCET 2007 Easy
- The angle between \(y^{2}=4 x\) and \(x^{2}+y^{2}=12\) at a point of their intersection isKCET 2011 Hard
- The value of \( \sin \left(2 \sin ^{-1} 0.8\right) \) is equal toKCET 2014 Hard
- \(\lim _{\mathrm{n} \rightarrow \infty} \mathrm{n} \sin \frac{2 \pi}{3 \mathrm{n}} \cdot \cos \frac{2 \pi}{3 \mathrm{n}}\) isKCET 2010 Easy
- If \( \tan ^{-1}\left(x^{2}+y^{2}\right)=\alpha \) then \( \frac{d y}{d x} \) is equal toKCET 2016 Medium
- If the circle \(\mathrm{x}^{2}+\mathrm{y}^{2}=\mathrm{a}^{2}\) intersects the hyperbola \(\mathrm{xy}=\mathrm{c}^{2}\) in four points \(P\left(x_{1}, y_{1}\right), Q\left(x_{2}, y_{2}\right), R\left(x_{3}, y_{3}\right)\) and \(S\left(x_{4}, y_{4}\right)\), thenKCET 2009 Medium
More PYQs from KCET
- G P Thomson experimentally confirmed the existence of matter waves by the phenomenaKCET 2009 Easy
- Match the entires in Column-I with those of Column-II and choose the correct answer.
Column-I Column-II A. Cleistogamy m. Insect pollination B. Geitonogamy n. Bud pollination C. Entomophily o. Pollination between flowers in the same plant D. Xenogamy p. Wind pollination q. Cross pollination KCET 2012 Medium - Polymerisation of DNA nucleotides during the synthesis of lagging strand occurs inKCET 2017 Easy
- 8.8 g of monohydric alcohol added to ethyl magnesium iodide in ether liberates \(2240 \mathrm{~cm}^3\) of ethane at STP. This monohydric alcohol when oxidised using pyridinium-chloro-chromate, forms a carbonyl compound that answers silver mirror test (Tollen's test). The monohydric alcohol isKCET 2024 Hard
- As the organic matter increases in a water body, the BODKCET 2017 Hard
- A candle placed \( 25 \mathrm{~cm} \) from a lens forms an image on a screen placed \( 75 \mathrm{~cm} \) on the other side
of the lens. The focal length and type of the lens should beKCET 2018 Medium