Question:
The eccentricity of an ellipse, with its centre at origin, is \(1/2\). If one of the directrices is \(x=4\), then the equation of the ellipse is
The eccentricity of an ellipse, with its centre at origin, is \(1/2\). If one of the directrices is \(x=4\), then the equation of the ellipse is
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Directrix distance \(=a/e\).
Updated On: Mar 23, 2026
- \(4x^2+3y^2=1\)
- \(3x^2+4y^2=12\)
- \(4x^2+3y^2=12\)
- \(3x^2+4y^2=1\)
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The Correct Option is C
Solution and Explanation
Step 1: For ellipse: \[ \text{directrix }=\frac{a}{e} \Rightarrow a=2 \]
Step 2: \[ b^2=a^2(1-e^2)=3 \]
Step 3: \[ \frac{x^2}{4}+\frac{y^2}{3}=1 \Rightarrow 4x^2+3y^2=12 \]
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