Get Answers to all your Questions

header-bg qa

The minimum area of a triangle formed by any tangent   to   the   ellipse   \frac{x^{2}}{16}+\frac{y^{2}}{81}=1     and the co-ordinate axes is:

  • Option 1)

    12

  • Option 2)

    18

  • Option 3)

    26

  • Option 4)

    36

 

Answers (1)

best_answer

 

Standard equation -

\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}= 1
 

- wherein

a\rightarrow Semi major axis

b\rightarrow Semi minor axis

 

 Let P=\left ( 4\cos \theta, 9\sin \theta \right )

So, Tangent equation is 

\frac{x\cos \theta}{4}+\frac{y\sin \theta}{9}= 1

A=\left ( 4\sec \theta,0 \right )

B=\left (0, 9cosec \theta \right )

Area = \frac{1}{2}*4\sec \theta*9cosec \theta= \frac{18*12}{\sin 2\theta}\: \: is\: \: minimum.

For\: \: 2\theta = 90^{\circ}\Rightarrow \theta = 45^{\circ}

Area =36

 

 


Option 1)

12

Option 2)

18

Option 3)

26

Option 4)

36

Posted by

satyajeet

View full answer

JEE Main high-scoring chapters and topics

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