# Thread: Plotting specific shapes for graphs.

1. ## Plotting specific shapes for graphs.

I'm interested in what shapes you can plot on a graph (cartesian co-ordinates) using an equation (1 line) like y=x......

I'm want to know if you can plot a cycloid on a graph with an equation....

2. ## Re: Plotting specific shapes for graphs.

A graph of the form y= f(x), where f is a function of f, cannot "turn back" on itself since by definition of "function", we cannot have more than one value of y for any x.

But the graph of $x^2+ y^2= R^2$ is a circle. The cycloid can be graphed using parametric equations x=a(t- sin(t)), y= a(1- cos(t)) or by using the single Cartesian equation $x= cos^{-1}(1- y/a)- \sqrt{y(2a- y)}$.

3. ## Re: Plotting specific shapes for graphs.

Thanks! Can you tell me what the variable a represents?