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Problem
Problem
Show that the locus of the middle points of normal chords of the parabola
y
2
=
4
a
x
y^2 = 4ax
y
2
=
4
a
x
is
y
4
−
2
a
(
x
−
2
a
)
y
2
+
8
a
4
=
0.
y^4 - 2a(x - 2a)y^2 + 8a^4 = 0.
y
4
−
2
a
(
x
−
2
a
)
y
2
+
8
a
4
=
0.
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