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

Answer

B, C

Explanation

Slope of tangent `=2`
the tangents are `y=2x+-sqrt(9xx4-4)`
i.e. `2x-y=+-4sqrt(4)`
`impliesx/(2sqrt(2))-y/(4sqrt(2))=1` and `(-x)/(2sqrt(2))+y/(4sqrt(2))=1`
Comparing it with `("xx"_(1))/9-(yy_(1))/4=1`
we get point of contact as `(9/(2sqrt(2)),1/(sqrt(2)))` and `(-9/(2sqrt(2)),1/(sqrt(2)))`