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The eccentricity of the conic x2- 4x + 4y2 = 4 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

As we learned

Eccentricity -

The ratio of a distance of point from focus to distance from fixed line.

- wherein

  It is donated by e.

The given conic is x2- 4x + 4y2 = 4. This equation can be written as

\left ( x-2 \right )^{2}+4\left ( y-0 \right )^{2}= 8

\Rightarrow \frac{\left ( x-2 \right )^{2}}{\left ( 2\sqrt{2} \right )^{2}}+ \frac{\left ( y-0 \right )^{2}}{\left ( \sqrt{2} \right )^{2}}= 1

This is an ellipse whose major and minor axes are

2a= 4\sqrt{2}\: \: and \: \: 2b=2 \sqrt{2}\: \: respectively.

Therefore, its eccentricity is given by

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

Posted by

Anam Khan

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