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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.


 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.

Grade:

1 Answers

noel thekkekara
31 Points
9 years ago

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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