The x -intercept of the common tangent to the parabolas y 2 = 32 x and x 2 = 108 y is

Question

The x -intercept of the common tangent to the parabolas y 2 = 32 x and x 2 = 108 y is, - 18, - 12, - 9, - 6

MARKS App · Accepted Answer

Tangent to y 2 = 32 x is y = m x + 8 m and tangent to x 2 = 108 y is y = m x - 27 m 2 ∴ 8 m = - 27 m 2 ⇒ m 3 = - 8 27 ⇒ m = - 2 3 ∴ x -intercept is 27 m = 27 - 2 3 = - 18

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