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 of

Vedclass · Accepted Answer

$\frac{\pi}{2}$

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 of the form $ax^2 + 2hxy + by^2 = 0$. Comparing the coefficients,we get: $a = \cos^2 	heta - 1 = -\sin^2 	heta$,$b = \sin^2 	heta$,$2h = -\sin^2 	heta \Rightarrow h = -\frac{1}{2} \sin^2 	heta$. Now,check the condition for perpendicular lines: $a + b = -\sin^2 	heta + \sin^2 	heta = 0$. Since the sum of the coefficients of $x^2$ and $y^2$ is zero $(a + b = 0)$,the lines represented by the equation 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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