What is the equation of a hyperbola with vertices (-5,0) and (5,0) and foci (-7,0) and (7,0) Please explain how to figure out whether it's a horizontal or vertical hyperbola?

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llltkl | College Teacher | (Level 3) Valedictorian

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The foci of the hyperbola has changing x-coordinates, hence it possesses a horizontal transverse axis.

By the midpoint formula, the center of the hyperbola occurs at the point (0, 0). Its foci are at (0+c, 0) and (0-c, 0). Hence c=(7-0)=7 and a=(5-0)=5

So, `b^2=(c^2-a^2)=(7^2-5^2)=24`

Therefore, the standard form of its equation is:

`(x-0)^2/25-(y-0)^2/24=1`

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

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