Convert the Equation to the Standard Form for an Ellipse $$4 x ^ { 2 } + 16 y ^ { 2 } + 8 x + 96 y + 84 = 0$$

question 122

Multiple Choice

Convert the equation to the standard form for an ellipse by completing the square on x and y.
- $$4 x ^ { 2 } + 16 y ^ { 2 } + 8 x + 96 y + 84 = 0$$

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

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Definitions:

Hypothesis

A supposition or proposed explanation made on the basis of limited evidence as a starting point for further investigation.

Prediction

The act of forecasting or estimating a future event based on current knowledge or analysis.

Theory

A systematic, coherent, and logical set of ideas about a particular topic or phenomenon that serves to organize and explain data and generate new knowledge.

Hypothesis

A hypothesis is a proposed explanation for a phenomenon, made as a starting point for further investigation, that can be tested through research and experimentation.