TS EAMCET · Maths · Ellipse
For an ellipse with eccentricity \(\frac{1}{2}\), the centre is at the origin. If one of its directrices is \(x=4\), then the equation of the ellipse is
- A \(3 x^2+4 y^2=12\)
- B \(3 x^2+4 y^2=49\)
- C \(3 x^2+4 y^2=1\)
- D \(4 x^2+3 y^2=12\)
Answer & Solution
Correct Answer
(A) \(3 x^2+4 y^2=12\)
Step-by-step Solution
Detailed explanation
\( \text { Given, } e=\frac{1}{2} \text { centre }(0,0) \text { and directrix }=4 \) \(\therefore\) Equation of ellipse \(=\frac{x^2}{a^2}+\frac{y^2}{a^2\left(1-e^2\right)}=1\)…
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