If one of the lines represented by $ax^2+2hxy+by^2=0$ bisects the angle between the positive coordinate axes,then

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:

For $\ell \in R$,the equation $(2 \ell-3) x^2+2 \ell xy-y^2=0$ represents a pair of distinct lines

If one of the lines represented by $ax^2+2hxy+by^2=0$ is perpendicular to $mx+ny=18$,then

Let $L_1, L_2$ be the lines represented by the equation $4x^2-5xy+3y^2=0$. Let $L_3, L_4$ be two lines passing through the point $(4,3)$ such that $L_3$ and $L_4$ are perpendicular to $L_1$ and $L_2$ respectively. If the combined equation of $L_3$ and $L_4$ is $ax^2+2hxy+by^2+2gx+2fy+c=0$,then find the value of $af+bg+ch$.

The equation of the pair of lines passing through the point $(2,1)$ and perpendicular to the pair of lines $4xy + 2x + 6y + 3 = 0$ is: