Find the locus of middle point of chord y2 = 4ax drawn through vertex.
y2 = 2ax
Let mid-point of the chord be (h, k) then equation of chord in mid-point from is
ky – 2a(x + h) = k2 – 4ah
As all these chords pass through the vertex hence it must satisfy (0, 0)
0 – 2i(0 + h) = k2 – 4ah
4ah – 2ah = k2
k2 = 2ah
Thus required locus is a parabola y2 = 2ax.
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