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Mathematics
Mathematics
Problem
Tangents are drawn to the hyperbola
x
2
9
−
y
2
4
=
1
\frac{x^2}{9} - \frac{y^2}{4} = 1
9
x
2
−
4
y
2
=
1
, parallel to the straight line
2
x
−
y
=
1
2x - y = 1
2
x
−
y
=
1
. The points of contact of the tangents on the hyperbola are a.
(
9
2
2
,
1
2
)
\left( \frac{9}{2\sqrt{2}}, \frac{1}{\sqrt{2}} \right)
(
2
2
9
,
2
1
)
b.
(
−
9
2
2
,
−
1
2
)
\left( -\frac{9}{2\sqrt{2}}, -\frac{1}{\sqrt{2}} \right)
(
−
2
2
9
,
−
2
1
)
c.
(
3
3
,
−
2
2
)
(3\sqrt{3}, -2\sqrt{2})
(
3
3
,
−
2
2
)
d.
(
−
3
3
,
2
2
)
(-3\sqrt{3}, 2\sqrt{2})
(
−
3
3
,
2
2
)
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