Identify this equation without completing the square.

Question

Identify this equation without completing the square.
x2 + y2 - 8x + 4y = 0

The equation defines a circle.
The equation defines an ellipse.
The equation defines a hyperbola.
The equation defines a parabola.

Answer 1

If A and C are not both 0, then a conic section with equation 

 

Ax^2 + Cy^2 + Dx + Ey + F = 0  is  

 

a  circle      if  A  = C

a parabola  if A*C = 0

an ellipse    if A ≠ C and A*C > 0

a hyperbola if A*C < 0

 

You have A = 1 and C = 1.