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# Find an equation in standard form for the hyperbola with vertices at (0, ±9) and foci at (0, ±10).

**Solution:**

Standard form of the equation of a hyperbola is

(x – h)^{2}/a^{2} - (y - k)^{2}/b^{2} = 1

Where (h, k) is the center = (0, 0)

Distance from center to vertices

a = 9 ⇒ a^{2} = 81

Distance from center to vertices which is given from the foci

c = 10

⇒ c^{2} = 100

Using the Pythagorean formula,

c^{2} = a^{2} + b^{2}

Substituting the values

100 = 81 + b^{2}

So we get,

b^{2} = 100 - 81 = 19

Substituting the values in the standard form

x^{2}/81 - y^{2}/19 = 1

Therefore, the equation of the hyperbola is x^{2}/81 - y^{2}/19 = 1.

## Find an equation in standard form for the hyperbola with vertices at (0, ±9) and foci at (0, ±10).

**Summary:**

The equation for the hyperbola with vertices at (0, ±9) and foci at (0, ±10) is x^{2}/81 - y^{2}/19 = 1.

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