Find the Center (H, K) and Radius R of the Circle

question 95

Multiple Choice

Find the center (h, k) and radius r of the circle with the given equation.
- $$4 x ^ { 2 } + 4 y ^ { 2 } - 12 x + 16 y - 5 = 0$$

• A) \(( \mathrm { h } , \mathrm { k } ) = \left( \frac { 3 } { 2 } , - 2 \right) ; \mathrm { r } = \frac { \sqrt { 30 } } { 2 }\)
• B) \(( \mathrm { h } , \mathrm { k } ) = \left( - \frac { 3 } { 2 } , 2 \right) ; \mathrm { r } = \frac { 3 \sqrt { 5 } } { 2 }\)
• C) \(( \mathrm { h } , \mathrm { k } ) = \left( - \frac { 3 } { 2 } , 2 \right) ; \mathrm { r } = \frac { \sqrt { 30 } } { 2 }\)
• D) \(( \mathrm { h } , \mathrm { k } ) = \left( \frac { 3 } { 2 } , - 2 \right) ; \mathrm { r } = \frac { 3 \sqrt { 5 } } { 2 }\)

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Definitions:

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The state of having sufficient financial resources to sustain a living without relying on employment, support from family, or governmental assistance.