# The normal #(2ap, ap^2)# to the parabola #x^2=4ay# meets the curve again at #Q(2aq, aq^2)#?

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(a) Show that #q=-(2+p^2)/p#

(b) Find the coordinates of P so that the lines #OP# and #OQ# meet at right angles, where #O# is the origin.

(a) Show that

(b) Find the coordinates of P so that the lines

##### 1 Answer

Nov 20, 2017

(a)Given equation of the parabola

Slope of the normal

Again the slope of the normal as it joins

So we have

OP and OQ being orthogonal the produt of their slopes

From (1) and (2) we get

(b)So coordinates of the point P will be