Final answer:
The surface represented by the equation is an elliptic cone.
Step-by-step explanation:
The given equation 7x² - 28y² + z² = 28 represents a surface known as an elliptic cone.
To identify it, we can compare the equation with the standard equation for an elliptic cone, which is Ax² - By² + Cz² = D. Since the coefficients of x², y², and z² are not equal, the equation represents an elliptic cone rather than a circular cone or a hyperbolic cone.
Therefore, the surface represented by the given equation is an elliptic cone.