Complete the Square to Determine Whether the Equation $y ^ { 2 } + 25 = 14 y - 16 x$

question 96

Essay

Complete the square to determine whether the equation $y ^ { 2 } + 25 = 14 y - 16 x$ represents an ellipse, parabola, hyperbola or 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 axis. 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:

Legally Subordinate

Refers to a legal status where an entity or individual is considered to have fewer rights or powers in comparison to another in a given legal context.

Planter Class

A social and economic class in the antebellum South, composed of wealthy landowners who owned plantations and many slaves.

Paternalistic

An approach or system where individuals in positions of authority restrict the freedom and responsibilities of those subordinate to them, purportedly in the latter's best interest.

Cultural Influences

The impact that one culture or society has on another, often leading to changes or developments in language, customs, values, and art.