The equation of the hyperbola whose foci are (6,4) and (-4,4) and eccentricity 2 is a.`((x-1)^2)/(25//4)-((y-4)^2)/(75//4)=1` b. `((x+1)^2)/(25//4)-((y+4)^2)/(75//4)=1` c. `((x-1)^2)/(75//4)-((y-4)^2)/(25//4)=1` d. none of these

Explanation

coordinates of centre are `(frac{6-4}{2}, frac{4+4}{2})`,i.e. `(1,4)`.


Let `2 {a}` and `2 {~b}` be the length of the transverse and the conjugate axes,


`Rightarrow frac{(x-1)^{2}}{a^{2}}-frac{(y-4)^{2}}{b^{2}}=1`


distance between the two foci `=2 a e`


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