All conic section can be written in the general form

\(\displaystyle{A}{x}^{2}+{B}{x}{y}+{C}{y}^{2}+{D}{x}+{E}{y}+{F}={0}\)

The conic section represented by an equation in general form can be determine the coefficient.

If coefficient is \(\displaystyle{B}^{2}-{4}{A}{C}<{0},{B}={0}{\quad\text{and}\quad}{A}={C}\), then its equation of circle.

If coefficient is \(\displaystyle{B}^{2}-{4}{A}{C}<{0},{B}\ne{0}{\quad\text{or}\quad}{A}\ne{C}\), then its equation of ellipse

If coefficient is \(\displaystyle{B}^{2}-{4}{A}{C}>{0}\), then its equation of hyperbola

If coefficicent is \(\displaystyle{B}^{2}-{4}{A}{C}={0}\), then its equation of ellipse

To find value of \(\displaystyle{B}^{2}-{4}{A}{C}\)

Compare general equation with given equation

Here \(\displaystyle{A}={16},{B}={0},{C}={9},{D}=-{98},{E}={5}{\quad\text{and}\quad}{F}={224}\)

\(\displaystyle{B}^{2}-{4}{A}{C}={0}^{2}-{4}{\left({16}\right)}{\left({9}\right)}=-{576}\)

Here \(\displaystyle{B}^{2}-{4}{A}{C}<{0},{\quad\text{and}\quad}{A}\ne{C}\)

Therefore ,the given equation as an ellipse.