Hi, 

 4x^2 - y^2 - 8x - 4y + 16 = 0   |Multiplying thru by -1

  y^2 + 4y - 4x^2 + 8x - 16 = 0

 (y+2)^2 -4  - 4[(x-1)^2 -1]  - 16 = 0

 (y+2)^2 -4  - 4(x-1)^2 +4  - 16 = 0

 (y+2)^2 - 4(x-1)^2 = 16

  C(1,-2) Vertices: (1,-6) and (1,2)

Domain: and Range: {y  ≤ -6 , y ≥ 2} 

 

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