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JEE Main202325 Jan 2023Morning ShiftMathematicsParabolaActual

The distance of the point 6 , - 2 2 from the common tangent y = m x + c , m > 0 , of the curves x = 2 y 2 and x = 1 + y 2 is

Options

  1. A1 3
  2. B5
  3. C14 3
  4. D5 3

Correct answer

B. 5

Step-by-step solution

Given, Equation of the curves x = 2 y 2 and x = 1 + y 2 Now for parabola y 2 = x 2 , equation of tangent is given by y = m x + 1 8 m Which is also tangent to parabola y 2 + 1 = x , So, y = m x + 1 8 m will satisfy the curve y 2 + 1 = x , Hence, mx + 1 8 m 2 + 1 = x ⇒ m 2 x 2 + 1 64 m 2 + x 4 + 1 = x ⇒ m 2 x 2 - 3 x 4 + 1 + 1 64 m 2 = 0 Now making discriminant zero we get, D = 0 ⇒ 3 4 2 - 4 × m 2 × 1 + 1 64 m 2 ⇒ 9 16 - 4 m 2 + 1 16 = 0 ⇒ m = 1 2 2 Hence, the equation of tange

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