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Consider a parabola defined by y² = 4λx, where λ is a positive constant, and let P be the endpoint of its latus rectum. An ellipse described by x²/a² + y²/b² = 1 also passes through P. If the tangents to the parabola and the ellipse at P intersect at a right angle, what is the eccentricity of the ellipse?
- √2/2
- 0.5
- 1/3
- 2/5
Correct answer: √2/2
Solution
The tangents to the parabola and ellipse at point P intersect at a right angle, which imposes a geometric constraint on the ellipse's eccentricity. Solving the equations for the tangents and using the given conditions yields an eccentricity of √2/2.
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