The eccentricity of the conic x^2 - 4 y^2 = 1, is - Vidyadip

MCQ

The eccentricity of the conic ${x^2} - 4{y^2} = 1$, is

A
$\frac{2}{{\sqrt 3 }}$
B
$\frac{{\sqrt 3 }}{2}$
C
$\frac{2}{{\sqrt 5 }}$
✓
$\frac{{\sqrt 5 }}{2}$

✓

Answer

Correct option: D.

$\frac{{\sqrt 5 }}{2}$

d
(d) Given conic is $\frac{{{x^2}}}{{{{(1)}^2}}} - \frac{{{y^2}}}{{{{\left( {\frac{1}{2}} \right)}^2}}} = 1$

$\therefore {b^2} = {a^2}({e^2} - 1)$

$⇒$ $\frac{1}{4} + 1 = {e^2}$

$⇒$ $e = \frac{{\sqrt 5 }}{2}$.

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