The point which divides the line in the ratio m:n externally is given by x =

Substituting the values we get,

x = which is undefined.

Distance between two points is given by

Therefore the distance from the origin to the point (x,y) is =

Vertical lines hve undefined slopes. Hence a line which is parallel to Y-axis has undefined slopes.

Equation of a line passing through (x1,y1) and (x2,y2)

=

Substituting the given values we get,

=

That is =

On cross multiplying and reaaranging we get,

bx - ay = 0

If this passes through the given point (a2,ab) then

b(a2) - a(ab) = 0

Let L be the foot of the perpendicular from the X axis. Therefore its y coocrdinate is zero Therefore the coordiantes of the point L is (x,0)

The vertical lines which are parallel to Y axis has undefined slopes. Hence the slope of the line 'm' will be undefined.

Therefore the above equation of the line will represent all lines through () except the line parallel to Y- axis

Since the angle made with x axis is zero, since tanθ is the slope. Then tan0 = 0 Hence the slpoe of the line parallel to X-axis is zero

Distance between parallel lines is given by

Now substituting the values we get,

=

The lines formed by these lines is right angled, triangle.

Two lines are perpendicular to each other if the product od their slopes is -1

Slope of the lines 3x - y – 4 = 0 , x + 3y – 4 = 0 are 3 and -1/3 respectively.

The product of these slopes is -1

Hence the lines3x - y – 4 = 0 , x + 3y – 4 = 0 are perpendicular to each other.

Therefore the triangle formed by these lines is a right angled triangle.

The given lines are paraallel lines

Condition for the line to be parallel is =

substituting the values,

=

Hence they are parallel lines.