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JEE Main201912 Jan 2019Evening ShiftMathematicsParabolaActual

The equation of a tangent to the parabola, x 2 = 8 y , which makes an angle θ with the positive direction of x - axis, is

Options

  1. Ay = x t a n θ + 2 c o t θ
  2. By = x t a n θ - 2 c o t θ
  3. Cx = y c o t θ + 2 t a n θ
  4. Dx = y c o t θ - 2 t a n θ

Correct answer

C. x = y c o t θ + 2 t a n θ

Step-by-step solution

As we know, if the line y = m x + c is a tangent to x 2 = 8 y = 4 × 2 × y , then c = - 2 m 2 . So, equation of tangent with slope m is y = m x - 2 m 2     . . . i Since, tangent is inclined at θ with the positive x - axis, i.e. m = tan ⁡ θ . Equation of tangent is y = t a n θ . x - 2 tan 2 ⁡ θ ⇒ y cot ⁡ θ = x - 2   t a n θ ⇒ x = y   c o t θ + 2   t a n θ

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