Rotate the Axes So That the New Equation Contains No $31 x^{2}+10 \sqrt{3} x y+21 y^{2}-144=0$

question 36

Multiple Choice

Rotate the axes so that the new equation contains no xy-term. Discuss the new equati
- $31 x^{2}+10 \sqrt{3} x y+21 y^{2}-144=0$

• A)
• \(\begin{array}{l}
• \theta=45^{\circ} \\
• x^{\prime 2}=-4 \sqrt{2} y^{\prime} \\
• \text { parabola } \\
• \text { vertex at }(0,0) \\
• \text { focus at }(0,-\sqrt{2}
• \end{array}\)
• B)
• \(\begin{array}{l}
• \theta=36.9^{\circ} \\
• \frac{x^{2}}{9}+\frac{y^{\prime 2}}{4}=1 \\
• \text { ellipse } \\
• \text { center at }(0,0) \\
• \text { major axis is } x^{\prime} \text {-axis } \\
• \text { vertices at }(\pm 3,0)
• \end{array}\)
• C)
• \(\begin{array}{l}
• \theta=30^{\circ} \\
• \frac{x^{\prime 2}}{4}+\frac{y^{\prime 2}}{9}=1 \\
• \text { ellipse } \\
• \text { center at }(0,0) \\
• \text { major axis is } y^{\prime} \text {-axi: } \\
• \text { vertices at }(0, \pm 3)
• \end{array}\)
• D)
• \(\begin{array}{l}
• \theta=45^{\circ} \\
• y^{\prime 2}=-4 \sqrt{2} x^{\prime} \\
• \text { parabola } \\
• \text { vertex at }(0,0) \\
• \text { focus at }(-\sqrt{2}, 0)
• \end{array}\)

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Definitions:

Ending Inventory

At the close of an accounting period, the financial worth of products available for sale, computed by starting with the inventory at the beginning, adding in purchases, and deducting the cost of goods sold.

Inventory Costing

The methodology for assigning costs to inventory items, which may include approaches like FIFO, LIFO, or average cost methods.

Ending Inventory

The value of goods available for sale at the end of an accounting period, calculated after considering the cost of goods sold.

Assets And Equity

Refers to the components of a company's balance sheet: assets represent what the company owns, and equity represents the owner's claims against those assets.