The angle between the lines represented by y^ | vedclass

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(D) The given equation is $x^2(\cos^2 	heta - 1) - xy \sin^2 	heta + y^2 \sin^2 	heta = 0$. This is a homogeneous equation of the second degree,whi

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$\frac{\pi}{2}$

Vedclass · Answer

(D) The given equation is $x^2(\cos^2 	heta - 1) - xy \sin^2 	heta + y^2 \sin^2 	heta = 0$. This is a homogeneous equation of the second degree,which can be compared with the general form $ax^2 + 2hxy + by^2 = 0$. Here,$a = \cos^2 	heta - 1 = -\sin^2 	heta$,$b = \sin^2 	heta$,and $2h = -\sin^2 	heta$. For a pair of lines represented by $ax^2 + 2hxy + by^2 = 0$,the lines are perpendicular if $a + b = 0$. Calculating $a + b$: $a + b = -\sin^2 	heta + \sin^2 	heta = 0$. Since $a + b = 0$,the lines are perpendicular to each other. Therefore,the angle between the lines is $\frac{\pi}{2}$.

The angle between the lines represented by $y^2 \sin^2 \theta - xy \sin^2 \theta + x^2(\cos^2 \theta - 1) = 0$ is

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