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.

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Definitions:

Ages 6-11

Refers to the developmental period known as middle childhood, characterized by physical, cognitive, and socioemotional changes.

Child Culture

The behaviors, norms, and practices shared among children, which can be distinct from adult culture.

Adult Morality

Refers to the sense of right and wrong, and the principles guiding decision-making and behavior, as developed and applied in adulthood.

Align

To place or arrange things in a straight line or in correct or appropriate relative positions.