Conics - Semi Major/Minor Axis

In summary, The conversation discusses finding the semi major and minor axis of an ellipse, with the center and foci already determined. The major axis is the line that joins the foci, while the minor axis is the line that goes through the center and is perpendicular to the major axis. The axis lengths can be found by using the formula and completing the squares routine. The values a and b in the formula \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1 indicate the lengths of the semi major and minor axes, respectively.
  • #1
katrina007
47
0
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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  • #2
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.
 
  • #3
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?
 
  • #4
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.
 
  • #5
yes i did that...but what do i read to tell the major/minor axes?
 
  • #6
So if you have it in the form
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]
a and b are what you need to look at.
 

1. What are conics and how are they related to semi major and minor axes?

Conics are a type of geometric shape that can be formed by the intersection of a plane and a cone. The semi major and minor axes are two important parameters that define the shape of a conic. They represent the longest and shortest distances from the center of the conic to its boundary, respectively.

2. How do you calculate the semi major and minor axes of a conic?

The semi major and minor axes can be calculated using the equation of the conic. For example, for an ellipse, the semi major axis is equal to half of the length of the major axis, while the semi minor axis is equal to half of the length of the minor axis.

3. What is the significance of the semi major and minor axes in conics?

The semi major and minor axes play a crucial role in determining the shape, size, and orientation of a conic. They also help in calculating other important parameters such as the eccentricity and focus of a conic.

4. How do changes in the semi major and minor axes affect the conic?

Changes in the semi major and minor axes can significantly alter the shape of a conic. For example, increasing the semi major axis of an ellipse will make it more elongated, while decreasing the semi minor axis of a hyperbola will make it more narrow.

5. Can the semi major and minor axes be negative?

No, the semi major and minor axes cannot be negative as they represent physical distances. However, they can be imaginary in certain cases, such as for a hyperbola with a complex eccentricity.

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