If the acute angle between the lines $ax^2+2hxy+by^2=0$ is $\frac{\pi}{4}$,then $4h^2=$

The measure of the acute angle $\theta$ between the pair of lines represented by the equation $2x^2 + xy - y^2 - x + 2y - 1 = 0$ is:

The equation $x^2-3xy+\lambda y^2+3x-5y+2=0$,where $\lambda$ is a real number,represents a pair of lines. If $\theta$ is the acute angle between the lines,then $\frac{\operatorname{cosec}^2 \theta}{\sqrt{10}} = $

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

If the slope of one of the pair of lines represented by $2x^2 + 3xy + Ky^2 = 0$ is $2$,then the angle between the pair of lines is

The angle between the lines represented by the equation $ax^2 + xy + by^2 = 0$ will be $45^\circ$,if