Question

Find the locus of the middle point of chords of parabola \(y^2 = 4ax\) which are normal to the parabola.

Answer 1

The answer given in the book is \(y^2(y^2 - 2ax + 4a^2) + 8a^4 = 0 \) . But, am not too sure how to go with this problem.

Answer 2

@iambatman @satellite73

Answer 3

@jim_thompson5910

Answer 4

when I use geogebra, I got this graph for y^2 = 4ax ('a' is some constant fixed number)