Angle Between Lines

If $y=mx$ bisects the angle between the lines $x^2(\tan^2\theta+\cos^2\theta)+2xy\tan\theta-y^2\sin\theta=0$ when $\theta=\dfrac{\pi}{3}$, then the value of $\sqrt{3}m^2+4m$ is

Lines $2x + 3y - 6 = 0$ and $9x + 6y - 18 = 0$ cut coordinate axes in concyclic points. Center of circle is:

If the lines x + (a – 1)y + 1 = 0 and 2x + a²y – 1 = 0 are perpendicular, then the condition satisfies by a is

If θ is acute angle between the pair of lines $x^2-7xy+12y^2=0$, then $\frac{2\cos \theta+3\sin \theta}{4\sin \theta+5\cos \theta}=$

For what values of $\lambda$ does the equation $6x^2 - xy + \lambda y^2 = 0$ represents two perpendicular lines and two lines inclined at an angle of $\pi/4$.

The obtuse angle between lines 2y = x + 1 and y = 3x + 2 is