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Let l 1 and l 2 be the two lines which are normal to y 2 = 4 x and tangent to x 2 = - 12 y respectively (where, l 1 and l 2 are not the x -axis). Then, the product of the slopes of l 1 and l 2 is

Options

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

Correct answer

B. 2

Step-by-step solution

Let the slope of the tangent be k , then the equation of the tangent to x 2 = - 12 y is k x = y + - 3 k 2 Let the slope of the normal be m , then the equation of the normal to y 2 = 4 x is y = m x - 2 m - m 3 ⇒ k = m and 2 m + m 3 = - 3 k 2 ⇒ m m 2 + 3 m + 2 = 0 ⇒ m = - 1 , - 2 ( m = 0 is rejected)

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