If one of the lines $2x^2 - xy + by^2 = 0$ passes through the point $(-4, -2)$,then $b^2 =$

The three sides of a triangle are given by the equation $(x^2+7xy+2y^2)(y-1)=0$. Find the centroid of the triangle.

The equation of one of the lines represented by the equation $x^2 + 2xy \cot \theta - y^2 = 0$ is

The joint equation of the pair of lines passing through the origin and forming an equilateral triangle with the line $y=5$ is

If the slopes of the lines represented by the equation $6x^2 + 2hxy + 4y^2 = 0$ are in the ratio $2:3$,then the value of $h$ such that both the lines make acute angles with the positive $X$-axis measured in the positive direction is

If $m_1$ and $m_2$ are the slopes of the lines represented by $ax^2 + 2hxy + by^2 = 0$ satisfying the condition $16h^2 = 25ab$,then $\ldots$.