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From a point P (h, k), in general, thre...

From a point `P (h, k)`, in general, three normals can be drawn to the parabola `y^2= 4ax`. If `t_1, t_2,t_3` are the parameters associated with the feet of these normals, then `t_1, t_2, t_3` are the roots of theequation at `at^2+(2a-h)t-k=0`. Moreover, from the line `x = - a`, two perpendicular tangents canbe drawn to the parabola. If the tangents at the feet `Q(at_1^2, 2at_1) and R(at_1^2, 2at_2)` to the parabola meet on the line `x = -a`, then `t_1, t_2` are the roots of the equation

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