Checkpoint: Identifying Conics Solution

Name the conic section. Explain.

$G : 4 x^{2} + 20 x y + 20 = 2 y^{2} + 9 x H : 5 x + 8 y = x^{2} + y^{2}$  

$4 x^{2} + 20 x y - 2 y^{2} - 9 x + 20 = 0 G : A = 4, C = - 2$  
Since A and C are non-zero and have opposite signs, equation G is a hyperbola.

  $x^{2} + y^{2} - 5 x - 8 y = 0 H : A = 1, C = 1$  
Since $A = C$ and are non-zero, equation H is a circle.

Note

You do not have to write the equation in the general form before naming the conic section, but it can be helpful if you have a sign error for A or C.