Question

# The angle between the lines given by the equation $$\displaystyle ay^{2}-\left ( 1+\lambda ^{2} \right )xy-ax^{2}=0$$ is same as the angle between the lines :

A
5x2+2xy3y2=0
B
x22xy3y2=0
C
x2y2=100
D
xy=0

Solution

## The correct options are B $$\displaystyle xy=0$$ C $$\displaystyle x^{2}-y^{2}=100$$Given pair of lines is $$\displaystyle ay^{2}-\left ( 1+\lambda ^{2} \right )xy-ax^{2}=0$$ Here, the sum of coefficients of $$x^2$$ and $$y^2$$ is $$0.$$Hence, the lines are perpendicular.Among the given options, C and D have sum of coefficients of $$x^2$$ and $$y^2$$ as $$0.$$Maths

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