Rotate the Axes to Eliminate The $x y$ -Term in the Equation

question 95

Multiple Choice

Rotate the axes to eliminate the $x y$ -term in the equation. Then write the equation in standard form.
$$113 x ^ { 2 } - 30 x y + 113 y ^ { 2 } - 6272 = 0$$

• A) \(\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 81 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 64 } = 1\)
• B) \(\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 49 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 36 } = 1\)
• C) \(\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 64 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 64 } = 1\)
• D) \(\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 49 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 49 } = 1\)
• E) \(\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 64 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 49 } = 1\)

---

Definitions:

Centralized

The concentration of control or authority in a single organization or location, often in the context of decision-making processes.

Hierarchy Of Authority

An organizational structure where different levels of power and responsibility determine how decisions are made and tasks are assigned.

Centralization

The degree to which decision-making authority is concentrated at higher levels within an organization.

Environmental Factors

External elements, conditions, or influences that impact an individual's behaviors, decisions, and wellbeing.