The eccentricity of an ellipse, with its centre at the origin, is $1 / 2$. If one of the directrices is…

The eccentricity of an ellipse, with its centre at the origin, is $1 / 2$. If one of the directrices is $\mathrm{x}=4$ then the equation of the ellipse is:
  1. $4 x^{2}+3 y^{2}=1$
  2. $3 x^{2}+4 y^{2}=12$
  3. $4 x^{2}+3 y^{2}=12$
  4. $3 x^{2}+4 y^{2}=1$

Solution

$\mathrm{e}=\frac{1}{2} .$ Directrix $, \mathrm{x}=\frac{\mathrm{a}}{\mathrm{e}}=4$ $ \therefore \mathrm{a}=4 \times \frac{1}{2}=2 \quad \therefore \mathrm{b}=2 \sqrt{1-\frac{1}{4}}=\sqrt{3} $ Equation of ellispe is $ \frac{x^{2}}{4}+\frac{y^{2}}{3}=1 \Rightarrow 3 x^{2}+4 y^{2}=12 $

Asked in: BITSAT 2015

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