AP EAMCET · Maths · Ellipse
The ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(b>a)\) and the parabola \(y^2=4 a x\) cut at right angles. If \(e\) is the eccentricity of the ellipse, then \(2 e^2=\)
- A 1
- B \(\frac{1}{2}\)
- C \(\frac{1}{8}\)
- D \(\frac{1}{3}\)
Answer & Solution
Correct Answer
(A) 1
Step-by-step Solution
Detailed explanation
Given equation of parabola is \(y^2=4 a x\), then slope of tangent to be given parabola at point of intersection \(\left(a t^2, 2 a t\right)\) is \(m_1=\frac{1}{t^{\prime}}\), and slope of tangent to the given ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) at point of…
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