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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

 Dec 12, 2020
 #1
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+1

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   

 

 

cool cool cool

 Dec 12, 2020

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