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anonymous
 one year ago
Find the equation of an ellipse with vertices (3, 0) and (3, 0) and foci of (2, 0) and (2, 0).
I dont know which formula to use!!! Please help me out?
anonymous
 one year ago
Find the equation of an ellipse with vertices (3, 0) and (3, 0) and foci of (2, 0) and (2, 0). I dont know which formula to use!!! Please help me out?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I know the answer to this question, its given in my textbook, but Im so confused on when to use which formula: The Major Axis Horizontal Formula? \[\frac{ x ^{2} }{ a ^{2} }+\frac{ y ^{2} }{ b ^{2} }\] Or the Major Axis Vertical Formula? \[\frac{ x ^{2} }{ b ^{2} }+\frac{ y ^{2} }{ a ^{2} }\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0First off, let's graph it.dw:1439370727299:dw

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0From our formula for an ellipse, \(\dfrac{(xh)^2}{a^2}+\dfrac{(yk)^2}{b^2}\) we find that our center lies at \((0,0)\), therefore our equation turns into: \[\frac{x^2}{a^2}+\frac{y^2}{b^2}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And if our center is greater than zero, we use the other formula?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0Secondly, just by graphing it, and looking at where our focus and vertices lie, we know that our ellipse is stretching horizontally, therefore \(a^2\) corresponds with \(x\) and \(b^2\) corresponds with \(y\)

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0We can now use the formula \(c^2=a^2+b^2\) to find our value of b.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0We have our value of \(a\), and that is the distance from the center to one of the vertices along the `major` axis. Therefore, \(a=3\)dw:1439371651892:dw

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0\(c\) is our distance from the center to one of the two foci. Therefore \(c=2\)dw:1439371729613:dw

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0using the pythagorean theorem, be can find \(b\). \[c^2=a^2+b^2 \iff b^2=c^2a^2\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0Do you see it now? With the given information, do you understand why I chose the formula I chose and how to input the information to find your equation?
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