Angle between the line joining the origin to the points of intersection of the curves 2x2+3y2+10x=0 and 3x2+5y2+16x=0 is
The equation of any curve through the points of intersection of the given curves is 2x2+3y2+10x+λ(3x2+5y2+16x)=0) ....(i)
If this equation represents two straight lines through the origin, then this must be homogeneous equation of second degree i.e., coefficient of x in (i) must vanish
∴10+16λ=0⇒=−1016=−58
Substituting this value of λ in (i), we get the equation of pair of straight lines x2−y2=0 .............(ii)
Hence the lines represented by the equation (ii) are mutually perpendicular.