The foci of the hyperbola `9x^2-16 y^2=144` are a.`(+-4,0)` b. `(0,+-4)` c. `(+-5,0)` d. `(0,+-5)`

Explanation

`Rightarrow frac{9 x^{2}}{144}-frac{16 y^{2}}{144}=1 `

`Rightarrow frac{x^{2}}{16}-frac{y^{2}}{9}=1`

`a=4` and conjugate axis `b=3`.
`e=frac{sqrt{a^{2}+b^{2}}}{a}`

`=frac{sqrt{4^{2}+3^{2}}}{4} `

`=frac{sqrt{16+9}}{4} `

`=frac{5}{4}`


the foci are `(5,0)` and `(-5,0)`.