Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If  and <img alt="\mathrm{ c_2 }" src="https://entrancecorner.oncodecogs.com/gif.late

If \mathrm{ c_1 } and \mathrm{ c_2 }  are the eccentricities of the ellipse, \mathrm{ \frac{x^2}{18}+\frac{y^2}{4}=1} and the hyperbola, \mathrm{\frac{x^2}{9}-\frac{y^2}{4}=1}  respectively and\mathrm{ \left(e_1, e_2\right)} is a point on the ellipse, \mathrm{ 15 x^2+3 y^2=k}, then k is equal to
 

Option: 1

14


Option: 2

15


Option: 3

17


Option: 4

16


Answers (1)

best_answer

\begin{aligned} &\mathrm{ Here, e_1=\sqrt{1-\frac{4}{18}}=\sqrt{\frac{7}{9}} and e_2=\sqrt{1+\frac{4}{9}}=\sqrt{\frac{13}{9}}}\\ &\mathrm{Since, \left(e_1, c_2\right) \text{is a point on the ellipse} 15 x^2+3 y^2=k}\\ &\mathrm{\therefore \quad 15 e_1^2+3 e_2^2=k \Rightarrow k=15\left(\frac{7}{9}\right)+3\left(\frac{13}{9}\right) \Rightarrow k=16}\\ \end{aligned}

Posted by

manish painkra

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

Amrita BTech Admission 2025: JEE Main-based registration deadline extended to August 30

Latest Question