Family of Straight Lines

The lines $(a+2\mathrm{b}) x+(a-3\mathrm{b}) y=a-b$ for different values of $a$ and $b$ pass through the fixed point whose coordinates are

What is the equation of the line passing through the point of intersection of the lines $x+2y-3=0$ and $2x-y+5=0$ and parallel to the line $y-x+10=0 ?$

The equation of the line passing through the point $\left(2,3\right)$ and the point of intersection of lines $2x-3y+7=0$ and $7x+4y+2=0$ is

The equation of a straight line passing through the point of intersection of the straight line $3x-y+2=0$ and $5x-2y+7=0$ and having infinite slope is

If non-zero numbers $a,b$ and $c$ are in $\mathrm{HP}$, then the straight line $\frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0$ always passes through a fixed point, that point is

The value of $k$ for which the lines $7x-8y+5=0, 3x-4y+5=0$ and $4x+5y+k=0$ are concurrent is given by

If the lines $x+3y-9=0, 4x+by-2=0$, and  $2x\mathit{-}y-4=0$ are concurrent, then the equation of the line passing through the point $\left(b,0\right)$ and concurrent with the given lines, is

Consider the family of lines $5x+3y-2+{\lambda }_1(3x-y-4)=0$ and $x-y+1+{\lambda }_2(2x-y-2)=0$. Equation of a straight line that belongs to both families is 

The values of $k$ for which lines $kx+2y+2=0, 2x+ky+3=0 \text{and} 3x+3y+k=0$ are concurrent

If $3a+2b+6c=0$, the family of straight lines $ax+by+c=0$ passes through a fixed point whose coordinates are given by