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  • <img alt="\mathrm{\text { The eccentricity of the conic } x^2-4 x+4 v^2=4 \text { is }}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Ctext%20%7B%20The%20eccentricity%20of%20t

\mathrm{\text { The eccentricity of the conic } x^2-4 x+4 v^2=4 \text { is }}

Option: 1

\frac{\sqrt{3}}{2}


Option: 2

\frac{2}{\sqrt{3}}


Option: 3

\sqrt{3}


Option: 4

none of these

 


Answers (1)

best_answer

The given conic is\mathrm{x^2-4 x+4 y^2=4}. This equation can be written as

\mathrm{\begin{aligned} (x-2)^2+4(y-0)^2 & =8 \\ & \frac{(x-2)^2}{(2 \sqrt{2})^2}+\frac{(y-0)^2}{(\sqrt{2})^2}=1 \end{aligned}}

This is an ellipse whose major and minor axes are \mathrm{2 a=2 \sqrt{2} \text { and } 2 b=\sqrt{2}} respectively.

Therefore, its eccentricity is given by 

\mathrm{e=\sqrt{1-\frac{b^2}{a^2}}=\sqrt{1-\frac{2}{8}}=\frac{\sqrt{3}}{2}}

 

 

Posted by

Ajit Kumar Dubey

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