Convert the Equation to the Standard Form for an Ellipse $$16 x ^ { 2 } + 4 y ^ { 2 } + 32 x + 24 y - 12 = 0$$

question 4

Multiple Choice

Convert the equation to the standard form for an ellipse by completing the square.
- $$16 x ^ { 2 } + 4 y ^ { 2 } + 32 x + 24 y - 12 = 0$$

• A) \(\frac { ( x + 3 ) ^ { 2 } } { 4 } + \frac { ( y + 1 ) ^ { 2 } } { 16 } = 1\)
• B) \(\frac { ( x + 1 ) ^ { 2 } } { 4 } + \frac { ( y + 3 ) ^ { 2 } } { 16 } = 1\)
• C) \(\frac { ( x - 1 ) ^ { 2 } } { 4 } + \frac { ( y - 3 ) ^ { 2 } } { 16 } = 1\)
• D) \(\frac { ( x + 1 ) ^ { 2 } } { 16 } + \frac { ( y + 3 ) ^ { 2 } } { 4 } = 1\)

---

Definitions:

Fine Arts

Disciplines involving the creation of artwork that is primarily appreciated for its aesthetic value and emotional power, including painting, sculpture, and music.

Construction

Construction refers to the process of building or assembling infrastructure, buildings, or any other substantial physical structures.

Communalist Orientation

A focus on the community and the collective over the individual, emphasizing shared values and responsibilities.

Cognitive Problems

Difficulties in processing information, including perception, memory, and reasoning, that can affect learning and day-to-day functioning.