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JEE Main201910 Apr 2019Evening ShiftMathematicsParabolaActual

If the line a x + y = c , touches both the curves x 2 + y 2 = 1 and y 2 = 4 2 x , then c is equal to:

Options

  1. A1 2
  2. B2
  3. C1 2
  4. D2

Correct answer

B. 2

Step-by-step solution

The equation of the tangent to the parabola y 2 = 4 a x is y = m x + a m . Hence, the equation of tangent to the parabola y 2 = 4 2 x is y = m x + 2 m       . . . 1 A line y = m x + c is a tangent to the circle x 2 + y 2 = r 2 if c 2 = r 2 1 + m 2 . Hence, the line 1 is also a tangent to the circle x 2 + y 2 = 1 , if 2 m 2 = 1 m 2 + 1 ⇒ m 2 m 2 + 1 - 2 = 0 ⇒ m 4 + m 2 - 2 = 0 ⇒ m 2 + 2 m 2 - 1 = 0 ⇒ m 2 = 1 since m 2 + 2 ≠ 0 ⇒ m = ± 1 . Thus, the equation of t

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