Homework Thread

[Treize]

My Teacher gave us a review, and we are supposed to to remember how to do it. I'm okay with everything but I don't remember how to graph Hyperbolas and Ellipses. I remember Ellipses being simple and Hyperbolas, needing to find the Foci, and Asymptotes. I just don't remember how to set it up at all.

Here is the equation for Hyperbola: 9x2 - 16y2 = 144 ( the 2s are supposed to be squared)

I don't need it solved I just need a refresh to remember.

I think it is easier for me to explain if I just solve it.

First you need to divide all the terms by 144 so that the equation equals 1.
You then have: 9x²/144 - 16y²/144 = 1

Then you divide the the numerator and the denominator of the x term by 9 and divide the numerator and the denominator of the y term by 16 so that the coefficient of x² and y² are 1.
You then have: x²/144/9 - y²/144/16 = 1
Which simplifies to: x²/16 - y²/9 = 1

Then you take the square root of each number in each term and instead square the whole term.
Which then equals: (x/4)² - (y/3)² = 1

Now you can graph it easily.

First you know that the hyperbola is going to open in the x direction because the x term is positive.

Now you draw the vertices. The vertices in this case would be at (4,0) and (-4,0) because you are dividing the x by 4 or you could think that the square roots of 16 from the previous equation are +4 and -4.

Now you have to draw the asymptotes. The points you would use to help draw the asymptote lines would be (4,3), (4,-3), (-4,3), and (-4,-3). because the square roots of 16 are +4 and -4 and the square roots of 9 are +3 and -3. These are basically for calculating the slopes of the lines, and you know that the asymptotes are going to go through the origin.

Now you connect the dots for your asymptote lines and draw your hyperbola.


Ellipses are much easier in my opinion.

Let's say we had the equation 9x² + 16y² = 144

From before you know that the equation would simplify to (x/4)² + (y/3)² = 1

Now this is pretty easy to graph.

First you start out at the origin and go 4 spaces to the left and right because you are dividing x by 4. Then you go 3 spaces up and down because you are dividing y by 3.

The points you would use are (4,0), (-4,0), (0,3), and (0,-3).

Finally you connect the dots for the ellipse.

I'm pretty sure this is all correct, but if someone knows more feel free to correct me. I haven't drawn ellipses and hyperbolas in awhile. If this doesn't make sense or something, I'll try to help some more.

Also, SOLDIER #819, if you still need help, I could try to help you. I've taken a Statistics class using a TI-83, so I might be able to help you out a little.