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Question

The coordinates of the point P on the curve y2 = 2x3,at which the tangent is perpendicular to the line 4x - 3 y + 2 = 0, are given by

A
(2, 4)
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B
(1, 2)
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C
(12, 12)
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D
(18, 116)
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Solution

The correct option is D (18, 116)
Differentiating y2=2x3, we get
2ydydx=6x2dydx=3x2y
The slope of the line 4x - 3y +2 = 0 is 43. Therefore, the coordinates of P(x, y) must satisfy
3x2y.43 = -14x2=y
Also, y2=2x3 . Solving these, we get x = 18and y = -116 (clearly x 0)

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