Identify the Center and Vertices of the Hyperbola $x ^ { 2 } - 16 y ^ { 2 } - 10 x - 96 y - 135 = 0$

question 89

Multiple Choice

Identify the center and vertices of the hyperbola. $x ^ { 2 } - 16 y ^ { 2 } - 10 x - 96 y - 135 = 0$

• A)center: (5,-3) vertices: \(( 1 , - 3 ) , ( 9 , - 3 )\)
• B)center: (-5,3) vertices: \(( - 5,2 ) , ( - 5,4 )\)
• C)center: \(( - 10,10 )\) vertices: \(( - 10,2 ) , ( - 10,10 )\)
• D)center: \(( 5 , - 3 )\) vertices: \(( 5 , - 4 ) , ( 5 , - 2 )\)
• E)center: \(( 10 , - 10 )\) vertices: \(( 10,24 ) , ( 10 , - 24 )\)

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Definitions:

Strike-Slip Fault

A type of fault where two blocks of Earth's crust slide past each other horizontally, often causing earthquakes.

Oblique-Slip Faults

Faults that combine features of both strike-slip and dip-slip faults, moving both horizontally and vertically.

Normal Fault

A type of fault where the hanging wall moves downward relative to the footwall due to tensional forces.

Reverse Fault

A type of fault where the hanging wall moves up relative to the footwall due to compressional forces.