Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Coordinate Geometry
0 votes

The line $x \cos \alpha + y \sin \alpha =p$ is a tangent to the ellipse. $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}$$=1$ if

$\begin{array}{1 1}(A)\;a^2 \cos ^2 \alpha -b^2 \sin ^2 \alpha =p^2 \\(B)\;a^2 \sin ^2 \alpha -b^2 \cos^2 \alpha =p^2 \\(C)\;a^2 \cos^2 \alpha + b^2 \sin ^2 \alpha =p^2 \\(D)\;a^2 \cos^2 \alpha+b^2 \sin ^2 \alpha=p \end{array}$

Can you answer this question?

1 Answer

0 votes
We know that line $y=mx+c$ is a tangent to the ellipse.
$c^2= a^2m^2 +b^2$
In this case $c= \large\frac{-p}{\sin \alpha}$
$m= \large\frac{- \cos \alpha}{\sin \alpha}$
So that given line will be a tangent if
$\large\frac{P^2}{\sin ^2 \alpha} $$=a^2 \large\frac{\cos ^2 \alpha}{\sin ^2 \alpha}$$+b^2$
$p^2=a^2 \cos ^2 \alpha +b^2 \sin ^2 \alpha$
Hence C is the correct answer.
answered Apr 10, 2014 by meena.p

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App