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  • If a tangent of slope ‘m’ at a point of the ellipse <img alt="\mathrm{\frac{x^2}{a^2}+\frac{y^2}{b^2}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%

If a tangent of slope ‘m’ at a point of the ellipse \mathrm{\frac{x^2}{a^2}+\frac{y^2}{b^2}} = 1 passes through (2a, 0) and if ‘e’ denotes the eccentricity of the ellipse then 

 

Option: 1

\mathrm{m^2+e^2=1}


Option: 2

\mathrm{2 m^2+e^2=1}


Option: 3

\mathrm{3 m^2+e^2=1}


Option: 4

none of these


Answers (1)

best_answer

Any tangent of slope m is  \mathrm{y=m x \pm \sqrt{a^2 m^2+b^2}} if it passes through (2 a, 0), then    \mathrm{3 a^2 m^2 =b^2 \Rightarrow 3 m^2=\frac{b^2}{a^2}=1-e^2}
Hence (C) is the correct answer.

Posted by

Rishabh

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