Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • A tangent drawn to the hyperbola   <img alt="\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}= 1\:

A tangent drawn to the hyperbola   \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}= 1\: \: at\: \: P\left ( \frac{\pi }{6} \right )   forms a triangle of area  3a^{2} sq. units with coordinate axes. Eccentricity of the hyperbola is equal to

Option: 1

\sqrt{17}


Option: 2

\sqrt{21}


Option: 3

4


Option: 4

\sqrt{6}


Answers (1)

best_answer

Using parametric form of tangent, the tangent at point P(\theta) is

\frac{x}{a}\sec \theta -\frac{y}{b}\tan \theta =1

If it meets the x-axis and y-axis at the points A and B respectively, then A\equiv \left ( a\cos \theta ,0 \right ),\: \: B\equiv \left ( 0,b\cot \theta \right )

\Delta _{OAB}= \frac{1}{2}ab.cos\theta .cot\theta=\frac{1}{2}ab\frac{\cos ^{2}\theta }{\sin \theta }

Put\,\,\theta=\frac{\pi}{6}

\Delta = \frac{1}{2}ab.\frac{3}{2}= 3a^2\,\,\,\,\,\,\,(Given)

\Rightarrow b=4a\Rightarrow 16a^{2}= a^{2}\left ( e^{2}-1 \right )\Rightarrow e= \sqrt{17}

Posted by

Sayak

View full answer

JEE Main high-scoring chapters and topics

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

Similar Questions