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Mathematics
Mathematics
Problem
Let
P
(
x
0
,
y
0
)
P(x_0,y_0)
P
(
x
0
,
y
0
)
be any point on the parabola
y
2
=
4
a
x
y^{2}=4ax
y
2
=
4
a
x
and let
P
′
(
x
0
,
−
y
0
)
P'(x_0,-y_0)
P
′
(
x
0
,
−
y
0
)
be its reflection in the axis of the parabola. If
F
(
a
,
0
)
F(a,0)
F
(
a
,
0
)
is the focus, prove that
P
F
=
P
′
F
PF = P'F
P
F
=
P
′
F
.
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