Graphing a function V.S. another function

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Homework Statement

Hi,

I'm really use to graphing a function vs x, were the x-axis would be the input to the function and the output would be the vertical function, were at each point on the graph would be the output evaluated at that particular x value

So I'm learning how to use MATLAB for my degree and the below is a exercise from my book

x_x(t) = t V_0 cos(theta)
x_y(t) = t V_0 sin(theta) + (a t^2)/2

were
x_x(t) = horizontal displacement of a projectile as a function of time in
x_y(t) = vertical displacement of a projectile as a function of time
t = 0:.01:20 s (all the values that occur by increments of .01 from 0 to 20)
theta = pi/4
a = -9.8 m/s^2

the particular exercise had me plotting x_y(t) V.S. x_x(t) on a graph, this is when I realized I had never done such a thing before were the x-axis is not the input and the y-axis is the output of some function evaluated at that particular x value... So I was wondering what exactly is the meaning of this graph, it's the vertical displacement that occurs at a particular horizontal displacement? Sense there evaluated at the same time values? but I was wondering if there was any way to come up with the function that describes the plot?

Homework Equations

The Attempt at a Solution

 

[Charles49]

These are called parametric equations.

Square both equations. Then add them. Simplify using the pythagorean identity. Try to recognize the resulting single equations as a circle = something.