Find the angle between the straight lines joining the origin to the point of intersection of `3x^2+5x y-3y^2+2x+3y=0` and `3x-2y=1`

Options

A. `(pi)/(3)`
B. `(pi)/(4)`
C. `(pi)/(6)`
D. `(pi)/(2)`

Answer

D

Explanation

The combined equation of the straight lines joining the origin to the points of intersection of `3x^(2)+5xy-3y^(2)+2x+3y=0 and 3x-2y=1` is
`3x^(2)+5xy-3y^(2)+(2x+3y)(3x-2y)=0`
`rArr" "9x^(2)+10xy-9y^(2)=0`
Clearly, it represents a pair of perpendicular straight lines.