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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 =
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
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
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.