The angle between the lines $y^{2} \sin ^{2} heta-x y \sin ^{2} heta+x^{2}\left(\cos ^{2} heta-1 ight)=0$ is

Question

The angle between the lines $y^{2} \sin ^{2} 	heta-x y \sin ^{2} 	heta+x^{2}\left(\cos ^{2} 	heta-1ight)=0$ is

Aicharya · Accepted Answer

We have $y^{2} \sin ^{2} 	heta-x y \sin ^{2} 	heta+x^{2}\left(\cos ^{2} 	heta-1ight)=0$ $	herefore\left(\sin ^{2} 	hetaight) y^{2}-\left(\sin ^{2} 	hetaight)(x y)-\left(\sin ^{2} 	hetaight) x^{2}=0$ $	herefore\left(\sin ^{2} 	hetaight)\left(y^{2}-x y-x^{2}ight)=0 \quad \Rightarrow \sin ^{2} 	heta=0 \Rightarrow 	heta=\frac{\pi}{2}$ Note : sum of coefficients of $x^{2}$ and $y^{2}$ is zero.

The angle between the lines $y^{2} \sin ^{2} \theta-x y \sin ^{2} \theta+x^{2}\left(\cos ^{2}…

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