The lines joining the origin to the points of intersection of the line 3x-2y -1 and the curve `3x^2 + 5xy -3y^2+2x +3y= 0`, are

Options

A. parallel to each other
B. perpendicular to each other
C. inclined at `45^@` to each other
D. None of these

Answer

B

Explanation

Given , equation of curves are `3x-2y=1`....(i)
and `3x^2+5xy-3y^2+2x+3y=0`....(ii)
Equation of lines joining point of intersection of Eqs. (i) and (ii) and origin is
`3x^2+5xy-3y^2+2x(3x-2y)+3y(3x-2y)=0`
`rArr 3x^2+5xy-3y^2+6x^2-4xy+9xy-6y^2=0`
`rArr 9x^2-9y^2+10xy=0`
Now , coefficient of `x^2+` coefficient of `y^2=9-9=0`
`therefore` Lines will be prependicular to each other.