Find the equations of the hyperbola satisfying the given conditions :Foci `(+-5,0)`, the transverse axis is of length 8.

Explanation

Since the foci of the given hyperbola are of the form `(+-c,0)` , it is a horizontal hyperbola .
Let the required be `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1.`
Length of its transverse axis = 2a.
`therefore 2a=8hArra=4hArra^(2)=16.`
Let its foci be `(+-c,0)`
then ,`c=5 [:' "foci are "(+- 5,0)]`
`therefore b^(2)=(c^(2)-a^(2))=(5^(2)-4^(2))=(25-16)=9.`
Thus , `a^(2)=16and b^(2)=9.`
Hence , the required equation is `(x^(2))/(16)-(y^(2))/(9)=1.`