Complete the Square to Determine Whether the Equation $\frac { 5 } { 2 } y ^ { 2 } + 5 y - \frac { 5 } { 4 } x ^ { 2 } + 5 x = \frac { 7 } { 2 }$

question 94

Essay

Complete the square to determine whether the equation $\frac { 5 } { 2 } y ^ { 2 } + 5 y - \frac { 5 } { 4 } x ^ { 2 } + 5 x = \frac { 7 } { 2 }$ 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:

Family Life Cycle

Stages through which a family progresses over time, from single individuals to married couples, parenthood, and retirement.

Entertainment Chasers

Individuals or groups who actively seek out new and exciting forms of entertainment, often through digital platforms or live events.

Devotees

Definition: Highly dedicated and loyal followers or fans of a particular brand, product, person, or concept.

Attention Seekers

Individuals or entities that actively pursue recognition, engagement, or notice from others, often through digital or social platforms.