Help with hyperbola question??

thank you so much!!!

The equation is:

(y - 5)^2 / 9  - (x - 4)^2/ 4  = 1         multiply both sides by 36

4(y - 5)^2  - 9(x - 4)^2   = 36       expand   

4(y^2 - 10y + 25) - 9(x^2 - 8x + 16)  = 36    simplify

4y^2 - 40y + 100 - 9x^2 + 72x  - 144  = 36

 4y^2  - 40y  -9x^2 + 72x - 80   = 0       to put in the proper form, multiply by -1 and rearrange

9x^2 - 4y^2 -72x + 40y + 80  = 0

Here's the graph of both forms......notice that they "overlay" each other......so......they are the same graph!!

https://www.desmos.com/calculator/i03ahreyrr

How did you know that was the equation Chris :/

I guess it is just one of life's mysteries.  :)