The locus of the middle points of normal chords of the parabola `y^2 = 4ax` is-

Explanation

we know, `t_2=-t_1-2/t_1` -(1)
`k=(2at_1+2at_2)/2`
`k/a=t_1+t_2`
from (1)
`K/a=t_1-t_1-2/t_1`
`t_1=(-2a)/k` -(2)
putting this value in equation (1)
`t_2=(2a)/k+k/a` -(3)
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