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Mathematics
Problem
The parabola
y
2
=
4
a
x
y^{2}=4ax
y
2
=
4
a
x
is required to pass through both the points
(
1
,
6
)
(1,6)
(
1
,
6
)
and
(
4
,
12
)
(4,12)
(
4
,
12
)
. Determine whether this is possible. If it is, find the value of
a
a
a
; if not, state why no such parabola exists.
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