JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If \(OB\) is the semi-minor axis of an ellipse, \(F_1\) and \(F_2\) are its foci and the angle between \(F_1B\) and \(F_2B\) is a right angle, then the square of the eccentricity of the ellipse is
- A \(\frac{1}{2}\)
- B \(\frac{1}{{\sqrt 2 }}\)
- C \(\frac{1}{{2\sqrt 2 }}\)
- D \(\frac{1}{4}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
Let \(\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1\) be he equation of ellipse. Given that \({F_1}B\) and \({F_2}B\) are perpandicluar to each other. Slope of \({F_1}B \times \) alop of \({F_2}B = - 1\)…
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