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Mathematics
Problem
If
y
1
,
y
2
,
y
3
y_1, y_2, y_3
y
1
,
y
2
,
y
3
be the ordinates of vertices of a triangle inscribed in a parabola
y
2
=
4
a
x
y^2 = 4ax
y
2
=
4
a
x
, then show that the area of the triangle is
∣
1
8
a
(
y
1
−
y
2
)
(
y
2
−
y
3
)
(
y
3
−
y
1
)
∣
\left| \frac{1}{8a} (y_1 - y_2)(y_2 - y_3)(y_3 - y_1) \right|
8
a
1
(
y
1
−
y
2
)
(
y
2
−
y
3
)
(
y
3
−
y
1
)
.
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