The area of the region enclosed between the pair of lines $xy = 0$ and the lines $xy + 5x - 4y - 20 = 0$ is .....

If the lines $x^2-4xy+y^2=0$ and $x+y=10$ contain the sides of an equilateral triangle,then the area of the equilateral triangle is

If $\frac{x^2}{a} + \frac{y^2}{b} + \frac{2xy}{h} = 0$ represents a pair of straight lines and the slope of one line is twice the other,then $ab : h^2$ is

If the centroid of the triangle formed by the lines $2y^2+5xy-3x^2=0$ and $x+y=k$ is $(\frac{1}{18}, \frac{11}{18})$,then the value of $k$ equals $..........$

Suppose the slopes $m_1$ and $m_2$ of the lines represented by $ax^2+2hxy+by^2=0$ satisfy $3(m_1-m_2)-7=0$ and $m_1m_2-2=0$. Then,which of the following is true?

If $P$ is the set of all real numbers $\alpha$ such that the product of the lengths of perpendiculars from $(\alpha, 1)$ to the pair of straight lines $3x^2+7xy+2y^2=0$ is $\frac{\sqrt{2}}{5}$,then the sum of the elements in $P$ is