Tangents are drawn to the hyperbola `x^2/9-y^2/4=1` parallet to the sraight line `2x-y=1.` The points of contact of the tangents on the hyperbola are (A) `(9/(2sqrt2),1/sqrt2)` (B) `(-9/(2sqrt2),-1/sqrt2)` (C) `(3sqrt3,-2sqrt2)` (D) `(-3sqrt3,2sqrt2)`

Options

A. `(+-(9)/(2sqrt(2)),+-(1)/(sqrt(2)))`
B. `(+-(1)/(sqrt(2)),+-(9)/(2sqrt(2)))`
C. `(3sqrt(3),-2sqrt(2))`
D. `(-3sqrt(3),2sqrt(2))`

Explanation

The points of contact of tangents of slope `m` to the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` are
`(+-(a^(2)m)/(sqrt(a^(2)m^(2)-b^(2))),+-(b^(2))/(sqrt(a^(2)m^(2)-b^(2))))`
Here , `m=2`, `a^(2)=9` and `b^(2)=4`.
So, the points of contact are
`(+-(18)/(sqrt(36-4)),+-(4)/(sqrt(36-4)))=(+-(9)/(2sqrt(2)),+-(1)/(sqrt(2)))`