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NTA Abhyas JEE Main2020MathematicsParabolaPractice

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

Options

A- 18
B- 12
C- 9
D- 6

Correct answer

A. - 18

Step-by-step solution

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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