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Tangents are drawn to the hyperbola $\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1$ , parallel to the straight line 2x-y=1.The points of contact of the tangents on the hyperbola are

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$(3 \sqrt{3}, - 2 \sqrt{2})$

$(\frac{9}{2 \sqrt{2}}, \frac{1}{\sqrt{2}})$

$(- 3 \sqrt{3}, 2 \sqrt{2})$

$(- \frac{9}{2 \sqrt{2}}, \frac{1}{\sqrt{2}})$

answer is A.

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Detailed Solution

Given hyperbola $\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1$

Given line 2x-y-1=0

Slope of tangent m=2

Point of contact

$= (\frac{\pm a^{2} m}{\sqrt{a^{2} m^{2} - b^{2}}}, \frac{\pm b^{2}}{\sqrt{a^{2} m^{2} - b^{2}}})$

$= (\frac{9}{2 \sqrt{2}}, \frac{1}{\sqrt{2}})$

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