Question

How do you write the equation of a hyperbola given vertices (-5, 0) and (5, 0) and foci (-7, 0) and (7, 0)?

Answer 1

`x^2/25-y^2/24=1`.

Explanation:

We know that, for the Hyperbola `S : x^2/a^2-y^2/b^2=1`,

the Focii and the Vertices are `(+-ae,0) and (+-a,0)`, resp.

Here, `e`, the Eccentricity of `S`, is given by, `b^2=a^2(e^2-1)`.

Clearly, in our case, `a=5, ae=7," so that, "e=7/a=7/5`.

`:. b^2=a^2(e^2-1)=25(49/25-1)=24`.

Hence follows the eqn. of `S : x^2/25-y^2/24=1`.