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JEE Main20198 Apr 2019Evening ShiftMathematicsParabolaActual

The tangent to the parabola y 2 = 4 x at the point where it intersects the circle x 2 + y 2 = 5 in the first quadrant, passes through the point:

Options

  1. A1 4 , 3 4
  2. B- 1 3 , 4 3
  3. C- 1 4 , 1 2
  4. D3 4 , 7 4

Correct answer

D. 3 4 , 7 4

Step-by-step solution

Let’s first find points of intersection of two curves. x 2 + 4 x = 5 ⇒ x = 1 ,   - 5 ( neglect x = - 5 ) Hence point of intersections are 1 ,   2 and 1 ,   - 2 . Tangent to the parabola at first quadrant point 1 ,   2 y ⋅ 2 = 2 x + 1 ⇒ y = x + 1 clearly point 3 4 , 7 4 satisfy the given equation of tangent.

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