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:

Capital Investment Analysis

The process of evaluating investments in physical assets to determine their potential for profit.

Sensitivity Analysis

Sensitivity Analysis is a financial modeling tool used to determine how different values of an independent variable affect a particular dependent variable under a given set of assumptions.

Expected Value Analysis

A statistical technique used to predict the likely outcome of a decision or series of actions by considering all possible scenarios and their probabilities.

Capital Rationing

The act of placing restrictions on the amount of new investments or projects a company may undertake, often due to limited resources such as capital.