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A hyperbola has vertices (±5, 0) and one focus (6, 0). What is the standard-form equation of the hyperbola?show steps

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The standard form of a hyperbola with center (h,k) is

We know the vertices are at (5,0) and (-5,0)

The vertices are at (h+a,k) and ( h-a,k)

The center must be at (0,0) and the a value is 5

The coordinates of the foci are at ( h+c,k) and ( h-c, k) and we know one of the foci is at (6,0)

c is equal to 6

We know that c^2 = a^2+b^2

6^2 = 5^2 + b^2

36 = 25+b^2

11 = b^2

We can write the equation

A hyperbola has vertices (±5, 0) and one focus (6, 0). What is the standard-form equation-example-1
A hyperbola has vertices (±5, 0) and one focus (6, 0). What is the standard-form equation-example-2
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