Question

If the lines joining origin to the points of intersection of the line $fx - gy = \lambda$ and the curve $x^{2} + hxy - y^{2} + gx + fy = 0$ be mutually perpendicular, then

• A. $\lambda = h$
• B. $\lambda = g$
• C. $\lambda = fg$
• D. $\lambda$may have any value

Answer 1

Answer: (D)

$\lambda$may have any value

Answer 2

Making the equation of curve homogeneous with the help of equation of line $\frac{fx - gy}{\lambda} = 1$and to be perpendicular to both the lines represented by this homogeneous equation

$a + b = 0 \Rightarrow \lambda + gf - \lambda - gf = 0 \Rightarrow 0 = 0$

Hence, $\lambda$may have any value.