Complete the Square to Determine Whether the Equation $x ^ { 2 } + 4 x - 8 y + 36 = 0$

question 15

Essay

Complete the square to determine whether the equation $x ^ { 2 } + 4 x - 8 y + 36 = 0$ represents an ellipse, a parabola, a hyperbola, or a 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 axes. 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:

Tariff

A tax on imports.

Subsidy

Financial support provided by the government to businesses, individuals, or other entities, aimed at promoting economic activities or ensuring the affordability of basic goods.

Tariffs

Taxes imposed by a government on imported goods in order to protect domestic industries or to generate revenue.

Quotas

A quota is a government-imposed trade restriction that limits the number or monetary value of goods that can be imported or exported during a specified period.