JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Consider the parabola \(P : y^2 = 4kx\) and the ellipse \(E : \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1\). Let the line segment joining the points of intersection of \(P\) and \(E\), be their latus rectums. If the eccentricity of \(E\) is \(e\), then \(e^2 + 2\sqrt{2}\) is equal to _____.
- A 2
- B 3
- C 4
- D 5
Answer & Solution
Correct Answer
(B) 3
Step-by-step Solution
Detailed explanation
The latus rectum of the parabola \(P: y^2 = 4kx\) is the line segment \(x = k\). The endpoints of this latus rectum are \((k, 2k)\) and \((k, -2k)\). The latus rectum of the ellipse \(E: \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1\) is the line segment \(x = ae\) (taking the one in…
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