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Mathematics
Mathematics
Problem
Consider the shifted hyperbola with center
C
(
2
,
3
)
C(2, 3)
C
(
2
,
3
)
given by
(
x
−
2
)
2
25
−
(
y
−
3
)
2
16
=
1
\frac{(x-2)^{2}}{25} - \frac{(y-3)^{2}}{16} = 1
25
(
x
−
2
)
2
−
16
(
y
−
3
)
2
=
1
. A tangent touches the hyperbola at point
T
T
T
and intersects the asymptotes at
A
A
A
and
B
B
B
. Calculate the perimeter of
△
C
A
B
\triangle CAB
△
C
A
B
given that the tangent is vertical (
x
=
7
x = 7
x
=
7
).
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