Question 875346
You should have no trouble identifying (b) and (c) as parabolas.  (a) takes more work unless you know another trick.


(a)
{{{ 25x^2+16y^2+150x=160y-225}}}
{{{25x^2+150x+16y^2-160y=-225}}}
Need Complete the Square
{{{25(x^2+6x)+16(y^2-10y)=-225}}}, this will most likely be an ellipse.
{{{25(x^2+6x+9)+16(y^2-10y+25)=-225+225+16*25}}}
{{{highlight_green(25(x+3)^2+16(y-5)^2=400)}}}
This is form enough to identify clearly an ellipse, although not yet finished into standard form.