The lines represented by the equation $x^2-y^2-x+3y-2=0$ are :

The lines ${a^2}{x^2} + bc{y^2} = a(b + c)xy$ will be coincident,if

If one of the lines of the pair $ax^{2}+2hxy+by^{2}=0$ bisects the angle between the positive direction of the axes,then $a, b,$ and $h$ satisfy the relation:

Let $PQR$ be an isosceles right-angled triangle with a right angle at $P(2, 1)$. If the equation of the line $QR$ is $2x + y = 3$,then the equation representing the pair of lines $PQ$ and $PR$ is:

The joint equation of a pair of lines passing through the point $(1, 4)$, where one line is parallel to the $X$-axis and the other makes an angle of $45^\circ$ with the positive direction of the $X$-axis, is:

The value of $\lambda$ with $|\lambda| < 16$ such that $2 x^2-10 x y+12 y^2+5 x+\lambda y-3=0$ represents a pair of straight lines,is