Show that the equation `n(ax+by+c)=c(lx+my+n)` represents the line joining the origin to the point of intersection of `ax+by+c=0 and lx+my+n=0`.

The equation ax+by+c=0 represents a straight line

Find the equation of the straight line which passes through the origin and the point of intersection of the lines ax+by+c=0 and a'x+b'y+c'=0 .

The condition that the equation lx +my +n = 0 represents the equatio of a straight line in the normal form is

Find the locus of the middle points of the segment of a line passing through the point of intersection of lines ax + by + c = 0 and lx + my + n = 0 and intercepted between the axes.

The equation ax+by +c=0 represents a plane perpendicular to the

If the ratio of the roots of the equation ax^(2)+bx+c=0 is m: n then

Find the locus of the circumcenter of a triangle whose two sides are along the coordinate axes and the third side passes through the point of intersection of the line a x+b y+c=0 and l x+m y+n=0.

The equations ax+by+c=0 and dx+ey+f=0 represent the same straight line if and only if

Find the condition that the ratio between the roots of the equation ax^(2)+bx+c=0 may be m:n.

Let the sides of a parallelogram be U=a, U=b,V=a' and V=b', where U=lx+my+n, V=l'x+m'y+n'. Show that the equation of the diagonal through the point of intersection of U=a, V=a' and U=b, V=b' " is given by " |{:(U,V,1),(a,a',1),(b,b',1):}| =0.