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Problem
Problem
A circle cuts the parabola
y
2
=
4
a
x
y^2 = 4ax
y
2
=
4
a
x
at right angles and passes through the focus, show that its centre lies on the curve
y
2
(
a
+
2
x
)
=
a
(
a
+
3
x
)
2
y^2(a + 2x) = a(a + 3x)^2
y
2
(
a
+
2
x
)
=
a
(
a
+
3
x
)
2
.
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