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JEE Main 2014

JEE Main 2014 Mathematics question on Conic Sections

The slope of the line touching both the parabolas y2=4xy^2 = 4x and x2=−32yx^2 = -32y is
  1. A.
    12\dfrac{1}{2}
  2. B.
    32\dfrac{3}{2}
  3. C.
    18\dfrac{1}{8}
  4. D.
    23\dfrac{2}{3}
Show answer and solution

Correct option: A

Solution

For y² = 4x, the tangent with slope m is y = mx + 1/m.

For x² = -32y, the tangent with slope m is y = mx + 8m².

For the same line to touch both parabolas: 1/m = 8m², giving m³ = 1/8, so m = 1/2.

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