Ask Questions, Get Answers

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

Find the condition of tangency for a line $y=mx+c$ touches the ellipse

$\begin{array}{1 1}(a)\;y=mx\pm \sqrt{a^2m^2+b^2}\\(b)\;y=mx\pm \sqrt{a^2m^2-b^2}\\(c)\;y=mx\pm \sqrt{am^2+b^2}\\(d)\;\text{None of these}\end{array}$

Can you answer this question?

1 Answer

0 votes
Now if line $y=mx+c$ is tangent than discriminant of the quadratic equation should be 0
Hence $(2mca^2)^2=4\times (c^2a^2-a^2b^2)(a^2m^2+b^2)$
$c=\pm \sqrt{a^2m^2+b^2}$
So line $y=mx+c$ touches the ellipse
$\large\frac{x^2}{a^2}+\frac{y^2}{b^2}$$=1$ if $c^2=a^2m^2+b^2$
Substituting c we get,
$y=mx\pm \sqrt{a^2m^2+b^2}$
Hence (a) is the correct answer.
answered Feb 7, 2014 by sreemathi.v

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