Question

The lines joining the points of intersection of line x + y = 1 and curve $x^2+y^2-2y+\lambda =0$ to the origin are perpendicular, then the value of $\lambda$ will be

• A. 1/2
• B. -1/2
• C.
• D. 0

Answer 1

The correct option is D

0

Making the equation of curve homogeneous with the help of line x + y =1,we get

$x^2+y^2-2y(x+y)+\lambda (x+y{)}^2=0$

$\Rightarrow x^2(1+\lambda )+y^2(-1+\lambda )-2yx=0$

Therefore the lines be perpendicular, if A + B = 0.

$\Rightarrow 1+\lambda -1+\lambda =0\Rightarrow \lambda =0$