SOLUTION: determine whether the following equations are parabolas,circles, ellipses or hyperbolas: (a) 25x^2+16y^2+150x=160y-225 (b) y^2-4x-4y+16=0 (c)(x+2)^2=y-3 Please I need t

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: determine whether the following equations are parabolas,circles, ellipses or hyperbolas: (a) 25x^2+16y^2+150x=160y-225 (b) y^2-4x-4y+16=0 (c)(x+2)^2=y-3 Please I need t      Log On


   

Question 875346: determine whether the following equations are parabolas,circles, ellipses or hyperbolas:
(a) 25x^2+16y^2+150x=160y-225
(b) y^2-4x-4y+16=0
(c)(x+2)^2=y-3

Please I need to solve this. Thank you !!
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
You should have no trouble identifying (b) and (c) as parabolas. (a) takes more work unless you know another trick.

(a)
+25x%5E2%2B16y%5E2%2B150x=160y-225
25x%5E2%2B150x%2B16y%5E2-160y=-225
Need Complete the Square
25%28x%5E2%2B6x%29%2B16%28y%5E2-10y%29=-225, this will most likely be an ellipse.
25%28x%5E2%2B6x%2B9%29%2B16%28y%5E2-10y%2B25%29=-225%2B225%2B16%2A25
highlight_green%2825%28x%2B3%29%5E2%2B16%28y-5%29%5E2=400%29
This is form enough to identify clearly an ellipse, although not yet finished into standard form.