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

Question 1026748: giving reasons, identify the following conic sections
i)16y=-4x^2+64
ii)4-4x-y=y^2+x^2
Answer by ikleyn(52792) (Show Source): You can put this solution on YOUR website!
.
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  = .

RELATED QUESTIONS
How do I algebraically determine where these two conic sections intersect?... (answered by Alan3354)

How can I algebraically find out where these two conic sections intersect?... (answered by Alan3354)

Identify the conic sections with the given equations. 1. 9x^2+9y^2-12x+24y-1=0 2.... (answered by Alan3354,josgarithmetic)

How do I solve the following system of conic sections??? x^2+y^2+2x+2y=0 and... (answered by ewatrrr)

Identify an axis of revolution and generating conic of the surface 4x^2 + 25y^2 + 4z^2 =... (answered by Alan3354)

x^2+4x=y-4 i must identify the conic. i think its a parabola is this correct.... (answered by solver91311)

separately(a) identify the conic and (b) give its center for each equation... (answered by Mathtut)

Identify the conic section for the equation. How can you tell the difference between the... (answered by fractalier)

Identify this conic section. 16y = x... (answered by Alan3354)