How to classify Conic Sections?

Quick Algebra 2, conic sections question. Please help.?

• Find the standard form of each equation by completing the square. Then identify and graph each conic. 25x^2-4y^2-72y-424=0

• Answer:

  25x^2 -4y^2 -72y = 424 25x^2 -4( y^2 + 18y) = 424 25x^2 -4( y^2 +18y +81) = 424-4*81 25x^2 -4(y+9)^2 = 100 (X^2)/4 - [(y+9)^2]/25 = 1 this is an hyperbola : C( 0, -9) It is horizontal with a= 2; b= 5, c= sqr(29) V( 0+/-2, -9)= (-2,-9) and (2,-9) Co-V( 0, -9+/-5) = (0,-14) and (0,-4) F(0+/- sqr(29), -9) = (-sqr29, -9) and (sqr29, -9) You will need to draw the asymptotes, also, in order to graph the hyperbola. Probably you use the method of locating the vertices, draw a rectangle around them, then the diagonals are the asymptotes. Hoping this helps!