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AP EAMCET202018 Sep 2020Morning ShiftMathematicsParabolaActual

The equation of the tangent to the parabola (y^2=12 x ), which makes an angle (30^ ) with the positive direction of (X )-axis is given by (x- 3 y+9=0 ), then its points of contact is

Options

  1. A((-9,-6 3 ) )
  2. B((9,-6 3 ) )
  3. C((-9,6 3 ) )
  4. D((9,6 3 ) )

Correct answer

D. ((9,6 3 ) )

Step-by-step solution

Let the point of tangency of tangent (x- 3 y+9=0 ) to the parabola (y^2=12 x ) is ( (x₁ y₁ ) ). Since equation of tangent to the parabola (y^2=12 x ) at point ( (x₁, y₁ ) ) is (y y₁=6 (x+x₁ ) ) (6 x-y₁ y+6 x₁=0 ), which represent the tangent (x- 3 y+9=0 ), so on comparing, we get ( 6 1 = -y₁ - 3 = 6 x₁ 9 (x₁, y₁ )=(9,6 3 ) ) Therefore, point of contact is ((9,6 3 ) ).

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