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

Question

The slope of the line touching both the parabolas y 2 = 4 x and x 2 = - 32 y is, 1 8, 2 3, 1 2, 3 2

MARKS App · Accepted Answer

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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