Write Equations of Rotated Conics in Standard Form
- $$x ^ { 2 } + 2 x y + y ^ { 2 } + x - y - 4 = 0$$

question 184

Multiple Choice

Write Equations of Rotated Conics in Standard Form
- $$x ^ { 2 } + 2 x y + y ^ { 2 } + x - y - 4 = 0$$

• A) \(x ^ { \prime 2 } = \frac { \sqrt { 2 } } { 2 } y ^ { \prime } + 2\)
• B) \(y ^ { \prime 2 } = \frac { \sqrt { 2 } } { 2 } x ^ { \prime }\)
• C) \(\frac { x ^ { \prime 2 } } { 2 } + \frac { y ^ { \prime 2 } } { 4 } = 1\)
• D) \(\frac { x ^ { \prime 2 } } { 2 } - \frac { y ^ { \prime 2 } } { 4 } = 1\)

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Definitions:

Quadratic Form

An expression in which the highest power of variables is squared, typically written in the form ax^2 + bx + c.

Square Root Property

A principle stating that for any positive number x, there exists a positive and negative value whose square equals x.

Square Root Property

Refers to a principle used to solve quadratic equations, stating that if \( x^2 = a \), then \( x \) is equal to both the positive and negative square root of \( a \).

Complex Solutions

Solutions to equations that include imaginary numbers, typically used when solving polynomial equations that do not have real-number solutions.