Question

Angle between the line joining the origin to the points of intersection of the curves $2x^2+3y^2+10x=0$ and $3x^2+5y^2+16x=0$ is

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is

D

The equation of any curve through the points of intersection of the given curves is $2x^2+3y^2+10x+\lambda (3x^2+5y^2+16x)=0)$ ....(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

$\therefore 10+16\lambda =0\Rightarrow \lambda =\frac{-10}{16}=\frac{-5}{8}$

Substituting this value of $\lambda$ in (i), we get the equation of pair of straight lines $x^2-y^2=0$ .............(ii)

Hence the lines represented by the equation (ii) are mutually perpendicular.