Condition for Collinearity of Three Points

Find the equations of the bisectors of the angle between the straight line $3 \mathrm{x}+4\mathrm{y}+2=0$ and $5\mathrm{x}-12\mathrm{y}-6=0$

Find the equation of the line which passes through the point of intersection of the lines $\mathrm{x}+2\mathrm{y}-3=0$ and $4\mathrm{x}-\mathrm{y}+7=0$ and is parallel to the line $\mathrm{y}-\mathrm{x}+10=0$

A firm produces $50$units of a good for $₹ 320$ and $80$ units for $₹ 380$. Supposing that the cost curve is a straight line, estimate the cost of producing $110$ units:

A straight line passes through the points $(\mathrm{a}, 0)$ and $(0, \mathrm{b})$. The length of the line segment contained between the axis is $13$ and the product of the intercepts on the axes is $60.$ Find the equation of the straight line :

Find the equation of the line passing through the point $(-4,-5)$ and perpendicular to the line joining the points $(1,2)$ and $(5,6)$ :

Find the equation of the lines which passes through the point $(3,4)$ and cuts off intercepts from the coordinate axes such that their sum is $14$.

A straight line$\frac{x}{a}-\frac{y}{b}=1$, passes through the point $(8, 6)$, and cut off a triangle of area $12 sq.units$, from the axes of coordinates.Find the equations of the straight line.

Find the equation of the line passing through the intersection of the lines $3x-4y+1=0$ and $5x+y-1=0$ and which cuts off equal intercepts from the axes.