Question

Find the equation of Hyperbola satisfying the following conditions: Foci `(pm5,0)` the transverse axis is of length 8.

Answer 1

Here, `2a=8rArra=4`
and `ae=5rArre=(5)/(4)`
`"Now", b^(2)=a^(2)(e^(2)-1)`
`=16((25)/(16)-1)=9`
Therefore, equation of hyperbola
`(x^(2))/(a^(2))-(y^(2))/(b^(2))=1rArr(x^(2))/(16)-(y^(2))/(9)=1`
`rArr9x^(2)-16y^(2)=144`