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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
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B
x22xy3y2=0
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C
x2y2=100
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D
xy=0
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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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