Complete the Square to Determine Whether the Equation $\frac { 1 } { 36 } x ^ { 2 } - \frac { 1 } { 2 } x + \frac { 153 } { 50 } + \frac { 1 } { 25 } y ^ { 2 } - \frac { 9 } { 25 } y = 1$

question 71

Essay

Complete the square to determine whether the equation $\frac { 1 } { 36 } x ^ { 2 } - \frac { 1 } { 2 } x + \frac { 153 } { 50 } + \frac { 1 } { 25 } y ^ { 2 } - \frac { 9 } { 25 } y = 1$ 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:

Competing Products

Products that are offered by different companies that serve the same market segment and meet the same needs or purposes as others.

Semantic Scales

A measurement scale used in research that assesses the connotative meaning of objects, concepts, or events, thus capturing the qualitative aspects of attitudes or feelings.

Consumer Perceptions

How consumers view and interpret the characteristics and qualities of a product or service, influencing their buying decisions.

Perceptual Map

A visual tool used in marketing to display the perceptions of consumers regarding the positions of products, brands, or companies relative to each other in the marketplace.