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Let the lines l 1 and l 2 be normals to y 2 = 4 x and tangents to x 2 = - 12 y (where l 1 and l 2 are not x -axis). The absolute value of the difference of slopes of l 1 and l 2 is

Options

  1. A3
  2. B2
  3. C1
  4. D1 2

Correct answer

C. 1

Step-by-step solution

The tangent to x 2 = - 12 y is k x = y + - 3 k 2 Normal to y 2 = 4 x is y = m x - 2 m - m 3 ⇒ k = m   &   2 m + m 3 = - 3 k 2 ⇒ m m 2 + 3 m + 2 = 0 ⇒ m = - 1 , - 2 ( m = 0 is rejected) Hence, the difference of slopes is equal to 1

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