Hey : )

identify the vertex, focus, and directrix of the parabola with the equation x^2 _ 6x _ 8y + 49 = 0

 parabola vertex form 
y= a(x-h)^2 + k => symmetry: x = h 
or x = a(y-k)^2 + h => symmetry: y = k 
(h,k) => vertex 
a = 1/4c 
c : distance between vertex and focus or directrix. 
 

x^2 – 6x – 8y + 49 = 0 
8y = x^2 - 6x + 49 = (x-3)^2-9+49 = (x-3)^2 + 40 
y= 1/8 (x-3)^2 + 5 
a = 1/8 = 1/4c 
c = 2 

vertex: (3, 5) 
focus: (3, 7) 
directrix: y = 3

I hope my answer has come to your help. Thank you for posting your question here in . We hope to answer more of your questions and inquiries soon. Have a nice day ahead!