Write the Equation of the Ellipse in Standard Form $$4 x ^ { 2 } + 16 y ^ { 2 } - 40 x + 96 y + 180 = 0$$

question 49

Multiple Choice

Write the equation of the ellipse in standard form. Identify the center and vertices.
- $$4 x ^ { 2 } + 16 y ^ { 2 } - 40 x + 96 y + 180 = 0$$

• A) \(\frac { ( x - 5 ) ^ { 2 } } { 16 } + \frac { ( y + 3 ) ^ { 2 } } { 4 } = 1\)
• center: \(( - 5,3 )\); vertices: \(( - 9,3 ) , ( - 1,3 )\)
• B) \(\frac { ( x - 5 ) ^ { 2 } } { 16 } + \frac { ( y + 3 ) ^ { 2 } } { 4 } = 1\)
• center: \(( 5 , - 3 )\); vertices: \(( 1 , - 3 ) , ( 9 , - 3 )\)
• C) \(\frac { ( x - 5 ) ^ { 2 } } { 4 } + \frac { ( y + 3 ) ^ { 2 } } { 16 } = 1\)
• center: \(( - 5,3 )\); vertices: \(( - 5,1 ) , ( - 5,5 )\)
• D) \(\frac { ( x - 5 ) ^ { 2 } } { 4 } + \frac { ( y + 3 ) ^ { 2 } } { 16 } = 1\)
• center: \(( 5 , - 3 )\); vertices: \(( 5 , - 5 ) , ( 5 , - 1 )\)

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Definitions:

Graph

A diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.

Logarithm

The exponent or power to which a base, typically 10 or e, must be raised to produce a given number; it is the inverse operation of exponentiation.

Graph

A visual diagram that exhibits the arrangement of connections or interrelations among several objects with the help of unique symbols including dots, lines, and bars.

Logarithmic Form

A way of writing exponential equations where the exponent is isolated on one side of the equation.