What is the Type and Orientation of Conics in Problems a and b?

camino
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Homework Statement



There are 2 problems a and b.
I've solved for both already.
I just need to know how to describe them by type and orientation.
In other words, what does what I got tell me in regards to type and orientation and how do I know this for future problems? (e.g. hyperbola or ellipse oriented vertically or horizontally)

a) (x-3)^2 (y-1)^2
-------- - -------- = 1
9 1

b) (x+1)^2 (y-1)^2
-------- + -------- = 1
25 4
 
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i see this didnt post right.
the 1 should be under the 2nd fraction in a)
the 4 should be under the 2nd fraction in b)
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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