Answer:
Hyperbola
Step-by-step explanation:
[tex]a,b \neq 0[/tex]
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex] is an ellipse.
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex] is a hyperbola.
[tex]\frac{(y-k)^2}{b^2}-\frac{(x-h)^2}{a^2}=1[/tex] is also a hyperbola.
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex] is a circle if [tex]a^2=b^2[/tex].
Notice the signs between each squared term.
It was the same sign for ellipse and circle (no minus; only plus).
It was different for hyperbola (+ to - for both).
