The angle between the lines joining origin to the points of intersection of the line `sqrt(3)x+y=2` and the curve `y^2-x^2=4` is `tan^(-1)(2/(sqrt(3)))` (b) `pi/6` `tan^(-1)((sqrt(3))/2)` (d) `pi/2`

Options

A. `tan^(-1)(2//sqrt3)`
B. `pi//6`
C. `tan^(-1)(sqrt3//2)`
D. `pi//2`

Answer

C

Explanation

Homogenizing the hyperbola using the straight line, we get equation of pair of straight lines OP and OQ, which is given by
`y^(2)-x^(2)=4((sqrt3x+y)/(2))^(2)`
`"or "y^(2)-x^(2)=3x^(2)+y^(2)+2sqrt3xy`
`"or "4x^(2)+2sqrt3xy=0`
`"or "x=0and 2x+sqrt3y=0`
Angle between the lines is
`(pi)/(2)-tan^(-1)((2)/(sqrt3))=tan^(-1)((sqrt3)/(2))`