JEE Main2014MathematicsApplication of DerivativesActual

The slope of the line touching both the parabolas y 2 = 4 x and x 2 = - 32 y is

Options

A1 8
B2 3
C1 2
D3 2

Correct answer

C. 1 2

Step-by-step solution

y 2 = 4 1 x x 2 = 4 - 8 y The equation of the tangent to y 2 = 4 x is y =   m x + a m The equation of the tangent to x 2 = 4 b y is   y =   m x - b m 2 Since, they have a common tangent, a m = - b m 2 ∴    1 m = 8 m 2 ∴     m 3 = 1 8 ∴     m = 1 2 ∴ The slope of the common tangent is 1 2 .

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