How To Make A Circle Graph
This video shows a simple explanation of how to take the numbers of a factorized or expanded math equation and use it to create an accurate graph of the circle it describes.
Hi, I'm Dr. Shah. I was the National Lecture Competition winner in 1989, and I'm the math master at Mathscool.
Now, ready for a new way of doing math? How to make a circle graph? I'm going to start with the equation of a circle. And it might look something like this. If you've seen an equation of a circle like that, it's in the factorized form.
And that's the best way if we want to graph here. Now, what we need to do is identify two things: one, the center of the circle and two, the radius of the circle. We can find the center of the circle simply by imagining each of these brackets as zero.
If this bracket were zero, the next would have to be minus five. So my 'x' would have to be minus five. And for this bracket to be zero, 'y' would have to be one.
So, one. Those are my x and y coordinates for the center of the circle. So from the brackets, you can easily identify the center of the circle.
And then I need to find the radius of the circle, and to find the radius of the circle, what I do is square root that, which is four as the radius of my circle. So there's my center and there's my radius, and now to graph that, I'm just going to start with a grid. I know the center is as minus five.
Minus one. Minus two. Minus three.
Minus four. Minus five. And a y coordinate of one.
One. So there's the center of my circle. And its radius is four.
So if I know its radius is four, I can already plot a few points. I know if I go to the right by four - One, Two, Three, Four - that's one point on the circle. Or to the left by four - one, two, three, four.
Down by four - one, two, three, four. And up by four - one, two, three, four. These are points on the circle, and I can just connect them together to form my circle.
There's the center of the circle, and its radius is four. That's the graph of a circle when the equation is given to us in factorized form. But what if the equation is given to us in expanded form? So I'll do an example like that now.
This is now written in expanded form. There are no brackets here, which means it's in expanded form. So what I need to do is collect together the x terms.
And then collect together the y terms. And then just leave that number at the end. Now, looking at the x terms, complete the square for these x terms.
So you now have to complete the square: x, half that number minus one squared, and then minus the square of that. So, it would be one. So, that's that one completed.
Again, I have to complete the square for this. So it's going to be y plus half that number- so two squared and then minus that square there. So two squared is four minus 24, equals 20.
Now, all I need to do is just collect these two numbers across to this side. So I'm going to add one and I'm also going to add four. Plus one and plus four.
Plus one and plus four. And so that gives me x minus 1 squared plus y plus two squared equals 25. And now, you see I've written it in factorized form which means you'd be able to identify the center of the circle, it's when x is one and when y is minus two.
And the radius is going to be the square root of that, which is five. And so again, that would now be easy for you to graph. .