Write an Equation for the Hyperbola $( 5 , - 10 )$

question 43

Multiple Choice

Write an equation for the hyperbola.
-center at $( 5 , - 10 )$ ; focus at $( 5 - 4 \sqrt { 10 } , - 10 ) ; e = \frac { 4 \sqrt { 10 } } { 12 }$

• A) \(\frac { ( x + 5 ) ^ { 2 } } { 144 } - \frac { ( y - 10 ) ^ { 2 } } { 16 } = 1\)
• B) \(\frac { ( x + 5 ) ^ { 2 } } { 16 } - \frac { ( y - 10 ) ^ { 2 } } { 144 } = 1\)
• C) \(\frac { ( x - 5 ) ^ { 2 } } { 144 } - \frac { ( y + 10 ) ^ { 2 } } { 16 } = 1\)
• D) \(\frac { ( x - 5 ) ^ { 2 } } { 16 } - \frac { ( y + 10 ) ^ { 2 } } { 144 } = 1\)