Complete the Square to Determine Whether the Equation $x ^ { 2 } + 4 x - 8 y + 36 = 0$

question 15

Essay

Complete the square to determine whether the equation $x ^ { 2 } + 4 x - 8 y + 36 = 0$ represents an ellipse, a parabola, a hyperbola, or a degenerate conic. Then sketch the graph of the equation. If the graph is an ellipse, find the center, foci, vertices, and lengths of the major and minor axes. If it is a parabola, find the vertex, focus and directrix. If it is a hyperbola, find the center, foci, vertices, and asymptotes. If the equation has no graph, explain why.

---

Definitions:

Municipal Debt Issues

Bonds or other forms of debt issued by municipalities to finance public projects.

Equity Capital

Funds raised by a company in exchange for shares of ownership.

Selling Bonds

The act of issuing debt securities by governments or corporations to investors in order to raise capital, with an obligation to pay back with interest.

Marketable Securities

Financial instruments that can be easily sold or bought on public stock and bond markets.