PN is the ordinate of a point P on the parabola y² = 4ax (N on the x-axis, A the vertex). A line parallel to the axis bisects NP and meets the parabola at Q. The line NQ meets the tangent at the vertex at a point T such that AT = k*NP. Find k.

Question

Accepted Answer

2/3. With P = (at², 2at), AT works out to 4at/3 and NP = 2at, so k = AT/NP = 2/3.

PN is the ordinate of a point P on the parabola y² = 4ax (N on the x-axis, A the vertex). A line parallel to the axis bisects NP and meets the parabola at Q. The line NQ meets the tangent at the vertex at a point T such that AT = k*NP. Find k.

Solution

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