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JEE Main20199 Jan 2019Morning ShiftMathematicsParabolaActual

Equation of a common tangent to the circle, x 2 + y 2 - 6 x = 0 and the parabola, y 2 = 4 x is:

Options

  1. A2 3 y = - x - 12
  2. B3 y = x + 3
  3. C3 y = 3 x + 1
  4. D2 3 y = 12 x + 1

Correct answer

B. 3 y = x + 3

Step-by-step solution

Let tangent to parabola y 2 = 4 x is y = m x + 1 m . . . i If equation ( i ) is tangent to given circle whose centre is ( 3 ,   0 ) and radius is 3 then length of perpendicular from centre of circle to equation ( i ) is equal to radius of circle. Hence, 3 m + 1 m m 2 + 1 = 3 ⇒ 3 m 2 + 1 = 3 m 1 + m 2 ⇒ 9 m 4 + 6 m 2 + 1 = 9 m 2 + 9 m 4 ⇒ m = ± 1 3 ∴ common tangents are y = x 3 + 3 or y = - x 3 - 3 ⇒ 3 y = x + 3   o r   3 y = - x - 3  

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