Identify the Foci and Write Equations for the Asymptotes $$9 ( y - 4 ) ^ { 2 } - 100 ( x + 4 ) ^ { 2 } = - 900$$

question 32

Multiple Choice

Identify the foci and write equations for the asymptotes.
- $$9 ( y - 4 ) ^ { 2 } - 100 ( x + 4 ) ^ { 2 } = - 900$$

• A) foci: \(( - 4 + \sqrt { 109 } , 4 ) , ( - 4 - \sqrt { 109 } , 4 )\)
• asymptotes: \(y = \frac { 10 } { 3 } x + \frac { 52 } { 3 }\) and \(y = \frac { 10 } { 3 } x - \frac { 28 } { 3 }\)
• B) foci: \(( 0 , - 4 + \sqrt { 109 } ) , ( 0 , - 4 - \sqrt { 109 } )\)
• asymptotes: \(y = \frac { 3 } { 10 } x - \frac { 14 } { 5 }\) and \(y = - \frac { 3 } { 10 } x - \frac { 26 } { 5 }\)
• C) foci: \(( 4 + \sqrt { 109 } , 0 ) , ( 4 - \sqrt { 109 } , 0 )\)
• asymptotes: \(y = \frac { 10 } { 3 } x - \frac { 28 } { 3 }\) and \(y = \frac { 10 } { 3 } x + \frac { 52 } { 3 }\)
• D) foci: \(( 0,4 + \sqrt { 109 } ) , ( 0,4 - \sqrt { 109 } )\)
• asymptotes: \(y = \frac { 3 } { 10 } x + \frac { 26 } { 5 }\) and \(y = - \frac { 3 } { 10 } x + \frac { 14 } { 5 }\)

---

Definitions:

Condition

A particular state of existence or a circumstance affecting the functioning of something or someone's health.

Excludes 1

A term used in coding and classification systems to indicate that conditions listed are not included within the section or code.

ICD-10-CM General Note

Guidelines and notes associated with the International Classification of Diseases, 10th Revision, Clinical Modification, used for coding and classifying morbidity data.

Mutually Exclusive Codes

Codes in a classification system that categorize information so that each item is assigned to only one category that does not overlap with others.