parabola

give me a few mins.. u will get the ans..

but to know what is wrong.. i need to know how u reached there!

seems a straightforward question...

two points be (at₁², 2at₁) and (at₂², 2at₂)

let the slope of the first from the origin(vertex) be m, -1/m (bcos perpendicular)

hence, 2at₁/at₁² = m
2/t₁ = m

and

2at₂/at₂² = -1/m

2/t₂ = -1/m

now it should be straighforward...

If u have reached uptil here, then there is some calculation mistake.. but i will finish this question in the next post

So, we have

t₁t₂ = - 4

midpoint is given by

{a(t₁²+t₂²)/2, a(t₁+t₂)}

let h,k be the locus...

h=a(t₁²+t₂²)/2
k=a(t₁+t₂)}

2h/a = t₁²+t₂²

(k/a)² = (t₁+t₂)²
= t₁²+t₂² + 2 t₁t₂

(k/a)² = 2h/a -8

Forgive my calculation or step mistakes if any :)