Question

Which equation represents the hyperbola that has its focus farthest from its center?

Answer 1

The distance the focus is from its center is noted as 'c' .

where  c^2 = a^2 + b^2.

Therefore whichever hyperbola has the largest ' a^2 +b^2 ' will have the largest 'c' value.

A)  8^2 + 7^2 = 113

B)  (19/2)^2 + (11/2)^2 = 120.5

C)  6^2 + 9^2  = 117
 
D) 5^2 + (19/2)^2 = 115.25

Answer is B