Determine if the graph of the equation below is a parabola, circle, ellipse, hyperbola, point, line, two lines, or empty. Enter the most specific answer.
y^2 - x^2 +5y - 25 = 0
Rearrange as
y^2 + 5y -x^2 = 25 complete the square on y
y^2 + 5y + 25/4 - x^2 = 25 + 25/4
(y +5/2)^2 - x^2 = 125/4 divide through by 125/4
( y + 5/2)^2 / (125/4) - x^2 / (125/4) = 1
This is a hrperbola that opens up /down