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