help 2

Q2  

x^2 - 6x - 2y + 7 = 0

Complete the square on 'x'

(x-3)^2 -9    - 2y+7 = 0      Move y and stuff to the right side of the equation

(x-3)^2 = 2y +2                  re-arrange to form

(x-3)^2 = 2 (y+1)

First one

Since the transverse axis  is parallel to the x axis  the hyperbola opens up and down

The form  is

( y - k)^2          (x  - h)^2

_______  -      ________   =     1

    a^2                  b^2

The center  is  ( h, k)  =  ( -3, 2)

The length of the transverse axis  = 2a  = 12

So....a   = 6

And 2b  = 8

So.....b  = 4

So  we have

( y - 2)^2           ( x +3)^2

________  -   __________   =   1

    36                      16

I wonder why cphill always put this at the end of his answers all the time