Question

What is the equation of a hyperbola with a = 8 and c = 20? Assume that the transverse axis is horizontal.

Answer 1

`(x^(2) )/(64) -(y^(2) )/(336) =1`

Explanation:

The equation of hyperbola is given by:

`(x^(2) )/(a^(2) ) -(y^(2) )/(b^(2) )`

Where
`c^(2) =a^(2) +b^(2)`

∵
`a=8,c=20`

∴
`b^(2) =c^(2) -a^(2)`

⇒
`b= \sqrt{20^(2) -8^(2) } =4√(21)`

Now,
`(x^(2) )/(a^(2) ) -(y^(2) )/(b^(2) ) =1`

⇒
`(x^(2) )/(8^(2) ) -(y^(2) )/(y(4√(21) )^(2) ) =1`

⇒
`(x^(2) )/(64) -(y^(2) )/(336) =1`

Hence, equation is
`(x^(2) )/(64) -(y^(2) )/(336) =1`

Hope this helps,

ROR