Conics - Semi Major/Minor Axis

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To find the semi-major and semi-minor axes of the ellipse given by the equation 25x^2 + 350x + 9y^2 - 54y + 1081 = 0, one must first complete the square to rewrite the equation in standard form. The center of the ellipse is determined to be at [7, 3], with foci located at [11, 3] and [3, 3]. The lengths of the semi-major and semi-minor axes can be identified from the standard form of the ellipse equation, specifically the values of a and b. These values are derived from the equation structured as (x-h)²/a² + (y-k)²/b² = 1, where a corresponds to the semi-major axis and b to the semi-minor axis. Understanding this relationship allows for the accurate identification of the axes lengths.
katrina007
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Hi,

I have this homework question and I completed and found the the foci and the center for the ellipse, but I don't understand how to find the semi major and minor axis.

Graph and give the center, semi major and semi minor axis and foci of the ellipse

25x^2 + 350x + 9y^2 - 54y +1081 = 0


For the center and Foci I got:
Center: [7, 3]
Foci: [11, 3] & [3, 3]

If anyone can help me with this, that'd be appreciated. Thanks in advance.
- Katrina
 
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The major axis is the line that joins the foci.
The minor axis is the line that goes through the center of the ellipse, and is perpendicular to the major axis.
 
i still don't know what the means or how to figure out the axis...can someone please tell me the axis and how they got it? do i need to use formula or something?
 
How did you find the center and foci? If you did the usual complete the squares routine then the axis lengths can be read off from that.
 
yes i did that...but what do i read to tell the major/minor axes?
 
So if you have it in the form
\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1
a and b are what you need to look at.
 

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