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A line y = mx (m > 0) intersects the parabola y² = x at a point P other than the origin. The tangent to the parabola at P meets the x-axis at Q. If the area of triangle OPQ is 4 square units, find m.

1. 1/2
2. 1/4
3. 1/8
4. 1/16

Correct answer: 1/2

Solution

P = (1/m², 1/m) and Q = (-1/m², 0). Area OPQ = (1/2)*base*height = (1/2)(1/m²)(1/m) = 1/(2 m³); setting this equal to 4 gives m³ = 1/8, so m = 1/2.

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