Expert: Paul Klarreich - 4/29/2007

Question
Hello Paul, I am currently taking College Algebra and Analytical Geometry. We are currently studying ellipses, hyperbolas,etc.. I have a quick question. :)

This is the problem I fighting with..

9(x-1)^2/16   (y 1)^2/9

How do I remove the coefficient 9, so it will be in standard form?    

Thanks for your help!
Karen

Answer
Questioner:   Karen
Category:  Advanced Math

Question:  Hello Paul, I am currently taking College Algebra and Analytical Geometry. We are currently studying ellipses, hyperbolas,etc.. I have a quick question. :)

This is the problem I fighting with..

9(x-1)^2/16   (y 1)^2/9

How do I remove the coefficient 9, so it will be in standard form?    

Thanks for your help!
Karen
.........................................
Hi, Karen,

************** VIEW IN COURIER FONT ***********

I think your example

9(x-1)^2/16   (y    1)^2/9

has some missing pieces:

9(x-1)^2/16   (y    1)^2/9
           +    +,-         = 1 ?

So if the example says:

9(x - 1)^2    (y + 1)^2
----------  + ---------- = 1
  16             9

Then all you need is to rewrite the first term:

9(....)   (....)
------- = -------
 16       16/9

Now your example looks like this:

(x - 1)^2    (y + 1)^2
---------  + ---------- = 1
 16/9           9

and it matches the standard form:

(x - h)^2    (y - k)^2
---------  + ---------- = 1
 a^2           b^2

with  a^2 = 16/9, and  a = 4/3  (Yes, fractions are legal.)
and  b^2 = 9,  b = 3