SOLUTION: What are the vertices of the following equation? {{{25x^2+250x-36y^2-576y=2579}}}

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: What are the vertices of the following equation? {{{25x^2+250x-36y^2-576y=2579}}}      Log On


   

Question 820267: What are the vertices of the following equation?
25x%5E2%2B250x-36y%5E2-576y=2579
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
What are the vertices of the following equation?
25x%5E2%2B250x-36y%5E2-576y=2579
complete the square:
25(x^2+10x+25)-36(y^2+16y+64)=2579+625-2304
25(x+5)^2-36(y+8)^2=900
%28x%2B5%29%5E2%2F36-%28y%2B8%29%5E2%2F25=1
This is an equation of a hyperbola with horizontal transverse axis.
Its standard form: %28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1, (h,k)=(x,y) coordinates of the center.
center:(-5,-8)
a^2=36
a=6
vertices:(-5±a,-8)=(-5±6,-8)=(-11,-8) and (1,-8)