Final answer:
The given equation represents an ellipse, which is one of the four conic sections that include circle, ellipse, parabola, and hyperbola, determined by the coefficients and signs in the general conic section equation.
Step-by-step explanation:
The conic section represented by the equation 5x²+9y²-80x+54y+221=0 is an ellipse. This determination can be made based on the presence of both x² and y² terms with coefficients that have the same sign, but are not equal, which is a characteristic of an ellipse. To clearly identify this, we would complete the square for both x and y terms.
The general equation for a conic section in the form Ax² + By² + Cx + Dy + E = 0 will yield a circle if A = B and there is no xy term present, an ellipse if A and B have the same sign and are not equal, a parabola if either A or B is zero, and a hyperbola if A and B have opposite signs.