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

1 Answer
Ratnaker Mehta
Feb 25, 2018

# 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#.

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