## How to write an equation for an ellipse using height and width

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mathpatient
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### How to write an equation for an ellipse using height and width

I need a refresher on writing ellipse equations. Here are two problems

Write the equation for an ellipse with center at (-4,7), height 5 and width 3.
[(x+4)^2/9] + [(y-7)^2/25] = 1

Write the equation for an ellipse with center at the origin, height 1/4 and width 1/3
16x^2 + 9y^2 = 1

The part that I forgot concerns how to understand the height and width - how to know when the
height and the width belong either under the x or the y.

I think that b is the semiminor axis and a is the semimajor axis, yet the the anwsers to these two
problems confuses me how to solve correctly. thanks for all your help
Last edited by mathpatient on Mon Jun 08, 2015 2:14 am, edited 1 time in total.

mathpatient
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Joined: Mon Jun 08, 2015 1:59 am
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### Re: How to write an equation for an ellipse using height and width

I might have a clue how to solve and I need to confirm with someone-
if the major axis is vertical then:
y^2/a^2 + x^2/b^2 = 1

if the major axix is horizontal then:
x^2/a^2 + y^2/b^2 = 1

so the larger number of the two - height or width indicates which is larger - the vertical axis or the horizonal which indicates the appropriate equation to use and whether a = height or a=width and conversely b=width or b=height

Might that be correct?

buddy
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### Re: How to write an equation for an ellipse using height and width

Yes (if you're saying that your a^2 is bigger than your b^2). It's like they show here.

mathpatient
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### Re: How to write an equation for an ellipse using height and width

Well I need some elaboration. If you look at the second problem and answer then I would think that a = 1/3 and b=1/4 and my answer would be the reverse of the answer given - I would say 9x^2 + 16y^2 =1. Could someone please illustrate each step to solve the problems for me?

buddy
Posts: 197
Joined: Sun Feb 22, 2009 10:05 pm
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### Re: How to write an equation for an ellipse using height and width

If you look at the second problem and answer then I would think that a = 1/3 and b=1/4 and my answer would be the reverse of the answer given
You're actually right and the answer they gave you is wrong. You can check by graphing. Look at the graph of their equation:

https://www.wolframalpha.com/input/?i=16x^2%2B9y^2%3D1

vs. the graph of your equation:

https://www.wolframalpha.com/input/?i=9x^2%2B16y^2%3D1

(Copy and paste the whole URLs. For some reason this forum can't process them??)