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Mathematics

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The difference between the x-coordinates of two points on the parabola y^2=4ax is fixed at 2k. Find the equation that describes the position(xp, py)of the point of intersection P of the tangents at the two points. The equation is in the form yp^2=f(xp).
Hence show that 4axp<yp^2<4axp+2k.

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