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Problem
Problem
The tangents to the parabola
y
2
=
4
a
x
y^2 = 4ax
y
2
=
4
a
x
at
P
(
a
t
1
2
,
2
a
t
1
)
P(at_1^2, 2at_1)
P
(
a
t
1
2
,
2
a
t
1
)
and
Q
(
a
t
2
2
,
2
a
t
2
)
Q(at_2^2, 2at_2)
Q
(
a
t
2
2
,
2
a
t
2
)
intersect at
R
R
R
. Prove that the area of the
Δ
P
Q
R
\Delta PQR
Δ
P
QR
is
1
2
a
2
∣
(
t
1
−
t
2
)
∣
3
\frac{1}{2}a^2|(t_1 - t_2)|^3
2
1
a
2
∣
(
t
1
−
t
2
)
∣
3
.
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