The lines represented by the equation $9x^2 + 24xy + 16y^2 + 21x + 28y + 6 = 0$ are

If the pair of lines given by $(x^2+y^2) \cos^2 \theta = (x \cos \theta + y \sin \theta)^2$ are perpendicular to each other,then $\theta$ is equal to

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

The number of values of $a$ for which the pair of lines represented by $3ax^2 + 5xy + (a^2 - 2)y^2 = 0$ are at right angles to each other,is

The pair of lines $l x^2 + 2(l+m) x y + m y^2 = 0$ lies along two diameters of a circle and divides the circle into $4$ sectors. If the area of the bigger sector is $5$ times the area of the smaller sector,then $\frac{l m}{(l+m)^2} = $

The lines represented by $ax^2 + 2hxy + by^2 = 0$ are perpendicular to each other,if ........