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Prove that the locus of the middle point of portion of a normal to y2 = 4ax intercepted between the curve & the axis is another parabola. Find the vertex & the latus rectum of the second parabola.
we take a point (at^2,2at) on the parabola
the normal is
y-2at=-t(x-at^2)
y-2at=-xt+at^3
on x axis y=0,(x-2a)t=at^3
x=a(2+t^3)
let the locus be (h,k)
now find midpoint get he relation between the points.
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