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

question 103

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

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Definitions:

Pragmatic Concerns

Practical considerations or limitations that affect how research or a policy can be implemented.

Type II Error

A statistical error that occurs when failing to reject a false null hypothesis; also known as a false negative.

α

The significance level in hypothesis testing, typically representing the probability of committing a Type I error.

Type II Error

The error that occurs when the null hypothesis is not rejected when it is actually false, also known as a "false negative".