peepsrock09
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Anyone know how to tell the difference between an ellipses equation versus a circle or hyperbola when graphing? 
Conic Sections
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I don't know what you mean by the difference between the equations "when graphing"...?peepsrock09 said:Anyone know how to tell the difference between an ellipses equation versus a circle or hyperbola when graphing?
To learn how to recognize from the equation what the graph will be, try the flowchart in this overview of conics.
fasteddie65
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Consider an equation in the form x^2/a^2 ± y^2/b^2 = 1.
If it is a +, it is either an ellipse or a circle. If a = b, it is a circle; if a ? b, it is an ellipse.
If it is a -, it is a hyperbola.
In a nutshell, that is how to tell.
That is not the whole story, but it may help.
If it is a +, it is either an ellipse or a circle. If a = b, it is a circle; if a ? b, it is an ellipse.
If it is a -, it is a hyperbola.
In a nutshell, that is how to tell.
That is not the whole story, but it may help.
D
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peepsrock09 said:Anyone know how to tell the difference between an ellipses equation versus a circle or hyperbola when graphing?
This is a topic that depends on - how far you want to know. For a detailed analysis, go to:
http://mathworld.wolfram.com/QuadraticCurve.html
Hello, peepsrock09!
\(\displaystyle \text{We are concerned with the coefficients of }x^2\text{ and }y^2.\)
\(\displaystyle \text{The general equation has: }\;Ax^2 + By^2 + \hdots\)
\(\displaystyle \text{(1) If }A = 0\text{ or }B = 0\text{, it is a }parabola.\)
. . .\(\displaystyle \text{(That is, only }one\text{ of the variables is squared.)}\)
\(\displaystyle \text{(2) If }A\text{ and }B\text{ have }opposite\text{ signs, it is a }hyperbola.\)
\(\displaystyle \text{(3) If }A\text{ and }B\text{ have the }same\text{ sign:}\)
. . .\(\displaystyle \text{if }A = B\text{, it is a }circle.\)
. . .\(\displaystyle \text{if }A \neq B\text{, it is an } ellipse.\)
\(\displaystyle \text{We are concerned with the coefficients of }x^2\text{ and }y^2.\)
\(\displaystyle \text{The general equation has: }\;Ax^2 + By^2 + \hdots\)
\(\displaystyle \text{(1) If }A = 0\text{ or }B = 0\text{, it is a }parabola.\)
. . .\(\displaystyle \text{(That is, only }one\text{ of the variables is squared.)}\)
\(\displaystyle \text{(2) If }A\text{ and }B\text{ have }opposite\text{ signs, it is a }hyperbola.\)
\(\displaystyle \text{(3) If }A\text{ and }B\text{ have the }same\text{ sign:}\)
. . .\(\displaystyle \text{if }A = B\text{, it is a }circle.\)
. . .\(\displaystyle \text{if }A \neq B\text{, it is an } ellipse.\)
You know what a circle looks like.
An ellipse looks like a circle that has been squished slightly.
A parabola is a single curve that is open, unlike a circle or ellipse.
A hyperbola is like a parabola that has been reflected in a mirror.
Looking at a graph of any of these, you should be able identify any of them immediately, unless it is an ellipse with a VERY small eccentricity, or somebody is trying to trick you by only showing you a portion of a graph (i.e. - only half of a hyperbola).
An ellipse looks like a circle that has been squished slightly.
A parabola is a single curve that is open, unlike a circle or ellipse.
A hyperbola is like a parabola that has been reflected in a mirror.
Looking at a graph of any of these, you should be able identify any of them immediately, unless it is an ellipse with a VERY small eccentricity, or somebody is trying to trick you by only showing you a portion of a graph (i.e. - only half of a hyperbola).