Need Help Ellipse and Hyperbola Equations  TOPIC_SOLVED

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Need Help Ellipse and Hyperbola Equations  TOPIC_SOLVED

Postby agenta1013 on Sun Nov 10, 2013 10:23 pm

I have two conic equations that I've been unable to put in standard form without getting at least one fraction, which messes up the rest of the steps.

The first:

I know this is an ellipse because the and terms have the same sign.

I need to put it in the standard form = 1 by factoring out terms and completing the square:



Completing the square causes this issue with the fraction in the x term:

Halving -3 and squaring it gets the fraction , so I get:



The right side simplifies to:



The y expression is an easy perfect square, so I get:



I can't get the x expression into a perfect square, and I've tried multiple approaches such as:


Dividing both sides by yields even more of a fraction mess, and I still can't get the numerators and isolated.

The second: --a hyperbola

After putting these in standard form, I need to find the center, vertices and foci--but I obviously can't do this until they're in standard form. Sorry about the length of this post, but I wanted to add everything I've tried so far. I'm about at my wit's end with these, so any help would be awesome!

Thanks :)
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Re: Need Help Ellipse and Hyperbola Equations

Postby nona.m.nona on Sun Nov 10, 2013 11:50 pm

Kindly please clarify how fractions are preventing a solution. Fractions, in and of themselves, are perfectly valid within the contexts of conic equations.
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Re: Need Help Ellipse and Hyperbola Equations

Postby little_dragon on Mon Nov 11, 2013 12:04 am

agenta1013 wrote:The first:

2x^2 - 6x + 3y^2 + 12y = 6
2(x^2 - 3x) + 3(y^2 + 2y) = 6
2(x^2 - 3x + 9/4) + 3(y^2 + 2y + 1) = 6 + 2(9/4) + 3(1)
2(x - 3/2)^2 + 3(y + 1)^2 = 6 + 9/2 + 3
2(x - 3/2)^2 + 3(y + 1)^2 = 27/2
2(2/27)(x - 3/2)^2 + 3(2/27)(y + 1)^2 = 1
(4/27)(x - 3/2)^2 + (2/9)(y + 1)^2 = 1
(x - 3/2)^2 / (27/4) + (y + 1)^2 / (9/2) = 1

so center (h,k) = (3/2, -1)
27/4=6.75
9/2=4.5
so a^2=27/4, b^2=9/2
a=3sqrt(3)/2, b=3/sqrt(2)

its messy but it works
:wave:
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Re: Need Help Ellipse and Hyperbola Equations

Postby agenta1013 on Tue Nov 12, 2013 2:35 pm

Thank you! :thumb:

This is confusing with fractions because there is no example in my textbook and the professor did not go over any examples of these with fractions either, only with simple whole numbers.
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Re: Need Help Ellipse and Hyperbola Equations

Postby buddy on Tue Nov 12, 2013 8:37 pm

& now you see why: stuff w/ fractions is messy! :lol:
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