- #1
alancj
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I’m having trouble graphing this equation:
16x^2+9y^2=144
I have entered it into both my Algebrator program and the quickmath.com website. They both gave the same graph of the ellipse. In each case the major axis was vertical. With the Algebrator program it simplifies the above equation into (quickmath.com didn’t do this):
(x^2)/9 + (y^2)/16 =1
This makes sense; just divide each side by 144 to make it all equal to 1. However, my textbook says that a^2 is always >/= to b^2. So the simplified equation seams to be wrong in the first place. If I try and use it to graph an ellipse myself then I find that the major axis would actually be shorter than the minor axis!
According to my textbook when the x term comes first the direction of the major axis is horizontal not vertical as was graphed by both programs.
In either case (horizontal or vertical form of the equation) the first term’s denominator is supposed to be a^2, and the next term’s denominator is b^2. That would mean that a=3 and b=4 and the length of the major axis would be 2a (6) and the minor would be 2b (8).
So this doesn’t make any sense, am I supposed to just graph this and ignore the fact that 2a is hardly “major” and 2b is hardly “minor”?
I don’t know of any other way of doing this problem. Any help would be much appreciated.
Thanks,
Alan
16x^2+9y^2=144
I have entered it into both my Algebrator program and the quickmath.com website. They both gave the same graph of the ellipse. In each case the major axis was vertical. With the Algebrator program it simplifies the above equation into (quickmath.com didn’t do this):
(x^2)/9 + (y^2)/16 =1
This makes sense; just divide each side by 144 to make it all equal to 1. However, my textbook says that a^2 is always >/= to b^2. So the simplified equation seams to be wrong in the first place. If I try and use it to graph an ellipse myself then I find that the major axis would actually be shorter than the minor axis!
According to my textbook when the x term comes first the direction of the major axis is horizontal not vertical as was graphed by both programs.
In either case (horizontal or vertical form of the equation) the first term’s denominator is supposed to be a^2, and the next term’s denominator is b^2. That would mean that a=3 and b=4 and the length of the major axis would be 2a (6) and the minor would be 2b (8).
So this doesn’t make any sense, am I supposed to just graph this and ignore the fact that 2a is hardly “major” and 2b is hardly “minor”?
I don’t know of any other way of doing this problem. Any help would be much appreciated.
Thanks,
Alan