Is this an ellipse or hyperbola

(x+10)^2/100 + (y-6)^2/81 =1

and how do you know?

It's an ellipse with its center at the point (-10,6). Its an ellipse because of the plus sign. It would be a hyperbola if it was

(x + 10)²/100 - (y - 6)²/81 = 1