SOLUTION: giving reasons, identify the following conic sections i)16y=-4x^2+64 ii)4-4x-y=y^2+x^2

1.  = .

   This equation is equivalent to

    = ,   or

    = .

   It is the equation of a parabola opened downward and symmetric about the vertical axis x = 0.

   Its vertex is V = (0, 4).  y-intercept is y = 4.  x-intercepts are x = -4 and x = 4.

 
  

  
 




Plot  = .

  
  

2.  = .

   This equation is equivalent to 

    = .

   Complete the squares in x and y separately. You will get an equivalent equation

    = ,   or

    = ,   or

    = .

   It is the equation of the circle with the center at  (x,y) = (-2,)  and the radius of  .

 
  

  
 




Plot  = .