Have you ever seen a graph, with a bunch of dots and lines on it? Maybe it was a graph of your growth, or of the temperature outside. Well, those dots and lines are made by plotting points on a coordinate system, which has two axes - a horizontal one and a vertical one.
Now, imagine drawing a line that goes through some of those dots. If you want to know where that line goes next, you could just keep following it until it hits the edge of the graph. But what if you wanted to know where the line goes even beyond the edge of the graph? That's where equations come in.
An equation is like a rule that tells you how to get the coordinates of any point on the line. For example, the equation y = 2x + 1 tells you that for any value of x, the corresponding y-value is 2 times x, plus 1. So if x is 0, then y is 1. If x is 1, then y is 3. And so on.
Now, what if the line wasn't just a straight line, but a curve? Well, we can still use an equation to describe it! We call it plane curve or parametric equation.
Let's take the example of a circle. A circle is a round shape, with every point on the edge of the circle the same distance away from the center. We can describe the circle with an equation: (x - a)^2 + (y - b)^2 = r^2. This equation tells us that for any point (x, y) on the circle, if we subtract the x-coordinate of the center (a) from x, and the y-coordinate of the center (b) from y, then square those differences and add them together, we get the radius of the circle (r) squared.
So, in short, a plane curve is like a rule that tells you how to get the coordinates of any point on a curve. It's a useful tool for understanding and describing different shapes and patterns in math.