A Conic Has Equation $32 x ^ { 2 } + 48 x y + 18 y ^ { 2 } - 14 x + y - 25 = 0$

question 45

Essay

A conic has equation $32 x ^ { 2 } + 48 x y + 18 y ^ { 2 } - 14 x + y - 25 = 0$ .
(a) Use the discriminant to identify the conic.
(a) by graphing the conic with a graphing calculator.
(b) Confirm your answer in part
(c) Find the angle necessary to eliminate the $x y$ - term.

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Definitions:

Net Operating Income

The total profit of a company after operating expenses are subtracted from gross profit but before taxes and interest are deducted.

Absorption Costing

Accounting method that includes all manufacturing costs - direct materials, direct labor, and both variable and fixed manufacturing overhead - in the cost of a product.

Unit Product Cost

The cost calculated per unit, combining all expenses including materials, labor, and overhead related to the production.

Variable Costing

A method of accounting that comprises solely of variable production expenses, such as direct materials, direct labor, and variable manufacturing overhead, in the calculation of product costs.