The equation ${y^2} - {x^2} + 2x - 1 = 0$ represents

If the equation $ax^{2} + by^{2} + cx + cy = 0$,$c \neq 0$ represents a pair of lines,then

If the sum of the slopes of the pair of lines represented by $4x^2 + 2hxy - 7y^2 = 0$ is equal to the product of the slopes,then the value of $h$ is

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.

If the angles made by the lines represented by the equation $ax^2 + 2hxy + by^2 = 0$ with the $X$-axis are $\alpha$ and $\beta$, then $\tan(\alpha + \beta)$ is

The values of $h$ for which the equation $3x^2 + 2hxy - 3y^2 - 40x + 30y - 75 = 0$ represents a pair of straight lines are: