a straight line parallel to the xaxis crosses the yaxis at y

Solution

In rectangular coordinates, as we know, the equation of a straight line is represented as y = mx + c, here c = L while the slope of the given line is zero, hence m = 0

That is y = L is the required equation of the line in rectangular coordinates.

Again for polar coordinates we know that:

y = r Sin

and x = r Cos

Now, for the given straight line y = L for all the values of , hence we can write:

L = r Sin

or r = L / Sin where varies from to zero.

Therefore the required equation in polar coordinates would r = L / Sin

NOTE: You might observe that if we sustitute this expression for r in the relation for x coordinate we would get

x = LCos/Sin which is an expected expression as for a straight line, if we multiply the Y coordinate with Cot where is the angle with the horizontal we would obtain the x coordinate.