Vertical or Horizontal ellipse?

In summary, the original conic was converted into standard form, with the equation being a vertical ellipse with the center at (-6, 2), and a=4 and b=3. The length of the major axis is 8, the length of the minor axis is 6, and the foci are located at (-6,-3) and (-6,7) with c=5. The value under y^2 is greater, indicating that it is a vertical ellipse. By graphing and calculating the lengths of the major and minor axes, it can be determined that this is a vertical ellipse.
  • #1
aisha
584
0
[tex] 16x^2+9y^2+192y-36y+468=0 [/tex]

Was the original conic i had to conver this into standard form and got

[tex] \frac {(x+6)^2} {9} + \frac {(y-2)^2} {16} =1 [/tex]

Im not sure if this is a horizontal or vertical ellipse
 
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  • #2
the center of the ellipse is [itex](-6, 2)[/itex]. If you get [itex]x=-6[/itex], then what range of values can [itex]y[/itex] take? If you set [itex]y = 2[/itex] then what range of values can [itex]x[/itex] take?

Can these facts help you to decide? If you can't see why they can directly, then draw a picture of the ellipse and see if you can tell~
 
  • #3
since the denominator of the x is less that the denominator of the y then the equation is in the form

[tex] \frac {(x-h)^2} {b^2} + \frac {(y-h)^2} {a^2} [/tex]

I think if what I said is right then this is a vertical ellipse

a=4 b=3?
 
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  • #4
indeed it is.
 
  • #5
Here are the features i got for this conic
Vertical ellipse
Center (-6,2) a=4 b=3
Length of major axis 2a=8
Length of minor axis 2b=6
Vertices (-6,-2) and (-6,6)
Foci=(-6,-3) and (-6,7) where c=5

are all of these correct?
:smile:
 
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  • #6
The focus is outsie of the ellipse? What is wrong? Is this ok?
 
  • #7
(h,-c+k) and (h,c+k) are the foci because this is a vertical ellipse

c=5 and I plugged in the center (-6,2) wats wrong?
 
  • #8
what's [itex]c[/itex], and why do you think it's [itex]5[/itex]?

If you're using it that way, then it should be [itex]\sqrt{7}[/itex] (I made a mistake earlier, by the way... that's why the other post is gone now :wink:)
 
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  • #9
c= sqrt(a^2+b^2) how is it sqrt7?
 
  • #10
it's actually

[tex]b^2 = a^2 - c^2 \Longrightarrow c^2 = a^2 - b^2 \Longrightarrow c = \sqrt{a^2-b^2}[/tex]

using your formula, you would always find the focii outside the ellipse.
 
  • #11
Thanks soo much I made the same mistake in 3 problems now I rememeber thankssssssss LIFE SAVER! :smile:
 
  • #12
If the value under y^2 is greater, then it's going to be a vertical ellipse.
If the value under x^2 is greater, then it's going to be horizontal.

You can check by graphing and calculating the lengths of the major and minor axes. That should help you too.
 

1. What is a vertical ellipse?

A vertical ellipse is a type of elliptical shape where the major axis is oriented vertically, meaning the longest distance across the shape is from top to bottom.

2. What is a horizontal ellipse?

A horizontal ellipse is a type of elliptical shape where the major axis is oriented horizontally, meaning the longest distance across the shape is from left to right.

3. How can you determine if an ellipse is vertical or horizontal?

An ellipse can be determined as vertical or horizontal by looking at the orientation of the major axis. If it is oriented vertically, it is a vertical ellipse, and if it is oriented horizontally, it is a horizontal ellipse.

4. What are the differences between a vertical and horizontal ellipse?

The main difference between a vertical and horizontal ellipse is the orientation of the major axis. This affects the shape and proportions of the ellipse, with a vertical ellipse appearing taller and narrower, and a horizontal ellipse appearing wider and shorter.

5. Can a vertical or horizontal ellipse be used to represent real-world objects?

Yes, both vertical and horizontal ellipses can be used to represent real-world objects, such as the orbits of planets around the sun or the shape of a water droplet. The orientation of the ellipse will depend on the orientation of the object in relation to the observer.

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