Find the vertices and foci of the hyperbola. 9x2 − y2 − 36x − 4y + 23 = 0

Hey there, hope I can help!

NOTE: Look at the image/images for useful tips



with the center of (h, k), semi-axis a and semi-conjugate - axis b.
NOTE: H = hyperbola




























Now rewrite in hyperbola standardform





Now we must compute c




Therefore the hyperbola foci is at 

For the vertices we have 

Simply refine it

Therefore the listed coordinates above are our vertices

Hope this helps!

Multiplication property of zero