JEE Main202226 Jul 2022Evening ShiftMathematicsParabolaActual

The equation of a common tangent to the parabolas y = x 2 and y = - x - 2 2 is

Options

Ay = 4 x - 2
By = 4 x - 1
Cy = 4 x + 1
Dy = 4 x + 2

Correct answer

B. y = 4 x - 1

Step-by-step solution

Let y = m x + c be the tangent to y = x 2 , then x 2 - m x - c = 0 For tangency, discriminant D = 0 ⇒ m 2 = - 4 c           … 1 Now let y = m x + c be also tangent to y = - x - 2 2 , then x - 2 2 + m x + c = 0 For D = 0 , we get m 2 - 8 m = 4 c             … 2 From 1 and 2 , we get m = 0 ,   c = 0 or m = 4 ,   c = - 4 So, there will be two common tangents y = 0 or y = 4 x - 4

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