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

Question

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

Aicharya · Accepted Answer

Equation of lines is $ x^2\left(\cos ^2 	heta-1ight)-x y \sin ^2 	heta+y^2 \sin ^2 	heta=0 $ This is a homogeneous equation of second degree, on comparing with $a x^2+2 h x y+b y^2=0$ $ \Rightarrow a=\cos ^2 	heta-1, \mathrm{~b}=\sin ^2 	heta, h=-\frac{1}{2} \sin ^2 	heta $ Now, $ \begin{aligned} a+b & =\cos ^2 	heta-1+\sin ^2 	heta \ & =1-1=0 \end{aligned} $ $\begin{array}{ll}	herefore & 	an 	heta=\frac{2 \sqrt{h^2-a b}}{a+b} \ \Rightarrow & 	an 	heta=\infty \Rightarrow 	heta=\frac{\pi}{2}\end{array}$

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

Solution