TS EAMCET · Maths · Ellipse
The ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(b>a)\) and the parabola \(y^2=8 a x\) cut at right angles. If \(e\) is the eccentricity of the ellipse, then \(e^4\) is equal to
- A \(\frac{1}{4}\)
- B \(\frac{1}{16}\)
- C \(\frac{1}{8}\)
- D \(\frac{1}{64}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{4}\)
Step-by-step Solution
Detailed explanation
(a) Given equation of ellipse is \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) ...(i) and equation of parabola is \(y^2=8 a x\) ...(ii) Differentiating Eq. (i) w.r.t \(x\), we get, \(\frac{2 x}{a^2}+\frac{2 y y^{\prime}}{b^2}=0\) \(\Rightarrow \quad y^{\prime}=-\frac{b^2 x}{a^2 y}\)…
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