## Question

A line bisecting the ordinate PN of a point P(at^{2}, 2at), t > 0 on the parabola y2 = 4ax, a > 0 is drawn parallel to the axis to meet the curve at Q. If NQ and the tangent at the point P meet at, T, then the coordinates of point T is (where point N lie on the axis)

### Solution

Coordinate of point

Equation of tangent at P, yt = x + at^{2},

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