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Parabola question

2020 · Shift 1 · Q22
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  2. /JEE Advanced
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  4. /Parabola
  5. /2020 · Shift 1 · Q22

Parabola question

2020 · Shift 1 · Q22

JEE AdvancedMathematicsParabolaMCQ+3 / −1
Let a, b and λ\lambdaλ be positive real numbers. Suppose P is an end point of the latus return of the parabola y2 = 4 λ\lambdaλ x, and suppose the ellipse x2a2+y2b2=1{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1a2x2​+b2y2​=1 passes through the point P. If the tangents to the parabola and the ellipse at the point P are perpendicular to each other, then the eccentricity of the ellipse is
  1. A
    12{1 \over {\sqrt 2 }}2​1​
  2. B
    12{{1 \over 2}}21​
  3. C
    13{{1 \over 3}}31​
  4. D
    25{{2 \over 5}}52​
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