Find the equations of the hyperbola satisfying the given conditions :Foci `(+-3sqrt(5),0)`, the latus rectum is of length 8.

Explanation

Here, `ae=3sqrt(5)`
and `(2b^(2))/(a)=8`
`rArrb^(2)=4a`
`rArra^(2)(e^(2)-1)=4a`
`rArra^(2)e^(2)-1a^(2)=4a`
`rArr45-a^(2)=4a`
`rArra^(2)+4a-45=0`
`rArr(a+9)(a-5)=0`
`rArra=-9anda=5`
But `a!=-9`
`:." "a=5`
`and" "b^(2)=4a=4xx5=20`
Therefore, equation of hyperbola
`(x^(2))/(25)-(y^(2))/(20)=1rArr4x^(2)-5y^(2)=100`