Complete the Square to Determine Whether the Equation $y ^ { 2 } + 25 = 14 y - 16 x$

question 96

Essay

Complete the square to determine whether the equation $y ^ { 2 } + 25 = 14 y - 16 x$ 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:

Cord

A unit of measure for wood, typically used for firewood or pulpwood, referring to a volume of 128 cubic feet.

Firewood

Wood that has been gathered or cut and is used primarily for fuel in a fire.

Pickup Truck

A vehicle with an enclosed cab and an open cargo area, usually with low sides and tailgate.

Mixed Numbers

A number consisting of an integer and a fractional part, commonly used in mathematics.