Complete the Square to Determine the Type of Curve Represented $4 x ^ { 2 } + 9 y ^ { 2 } - 16 x - 20 = 0$

question 53

Multiple Choice

Complete the square to determine the type of curve represented by the equation. $4 x ^ { 2 } + 9 y ^ { 2 } - 16 x - 20 = 0$

• A) \(\frac { ( x - 2 ) ^ { 2 } } { 9 } + \frac { ( y + 2 ) ^ { 2 } } { 4 } = 1\)
• , ellipse
• B) \(9 ( x - 2 ) ^ { 2 } - 4 y ^ { 2 } = 9\)
• , hyperbola
• C) \(\frac { x ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 4 } = 1\)
• , ellipse
• D) \(\frac { ( x - 2 ) ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 4 } = 1\)
• , hyperbola
• E) \(\frac { ( x - 2 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1\)
• , ellipse

---

Definitions:

Cognitive Dissonance

A psychological state of discomfort arising from holding two or more conflicting beliefs, values, or attitudes, leading to behavior change or attitude adjustment.

Consistency

is the tendency to maintain a uniform behavior, attitude, or belief over time.

Cognitions

Mental processes involved in gaining knowledge and comprehension, including thinking, knowing, remembering, judging, and problem-solving.

Motivated

Having a desire or willingness to achieve something, often accompanied by enthusiasm.