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jordo6889 · Oct 26, 2009, 01:55 PM

Find the equation in standard form of an ellipse with center at (0,0) minor axis of length 12, and foci at (0,-8) and (0,8).

Nhatkiem · Oct 26, 2009, 07:25 PM

Originally Posted by jordo6889

Find the equation in standard form of an ellipse with center at (0,0) minor axis of length 12, and foci at (0,-8) and (0,8).

the general standard form of an ellipse is

$(\frac{x}{a})^2+(\frac{y}{b})^2=1$

where a and b are the radii of your major and minor axis.:)

ebaines · Oct 27, 2009, 07:20 AM

Nhatkiem's suggestion will let you determine the value of b, but to find a you need to use the fact that :

$<br /> a^2 - b^c = F^2<br />$

where F is the distance from the center of the ellipse to the focal point(s).

Also, don't forget that a and b are the lengths of the semi-major and semi-minor axes, respectively.

Nhatkiem · Oct 27, 2009, 09:13 AM

Originally Posted by ebaines

Nhatkiem's suggestion will let you determine the value of b, but to find a you need to use the fact that :

$<br /> a^2 - b^c = F^2<br />$

where F is the distance from the center of the ellipse to the focal point(s).

Also, don't forget that a and b are the lengths of the semi-major and semi-minor axes, respectively.

hmm I always thought the definition for minor/major axis were dependent one which ones were longer, meaning the definition of a and b were interchangeable depending on lengths:confused: Been a while since I've done this ellipse.. boo.

ebaines · Oct 27, 2009, 09:25 AM

Originally Posted by Nhatkiem

hmm I always thought the definition for minor/major axis were dependent one which ones were longer, meaning the definition of a and b were interchangeable depending on lengths:confused: Been a while since ive done this ellipse .. boo.

Yes - you are right - the a dimension is along the x axis, and the b along the y axis. If a > b then a is the semi-major axis length and b is the semi-minor length. I jumped ahead a bit and said that a is the semi-major and b the semi-minor, essentially giving away that the ellipse is stretched horizontaly (not vertically). The point I was trying to make was to distinguish between the minor axis length and the semi-minor laxis ength.