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# Find an equation in standard form for the hyperbola with vertices at (0, ±3) and foci at (0, ±7).

**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 = 3

a^{2} = 9

Distance from center to vertices which is given from the foci

c = 7

c^{2} = 49

Using the Pythagorean formula

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

Substituting the values

49 = 9 + b^{2}

So we get

b^{2} = 49 - 9 = 40

Substituting the values in the standard form

x^{2}/9 - y^{2}/40 = 1

Therefore, the equation of the hyperbola is x^{2}/9 - y^{2}/40 = 1.

## Find an equation in standard form for the hyperbola with vertices at (0, ±3) and foci at (0, ±7).

**Summary: **

An equation in standard form for the hyperbola with vertices at (0, ±3) and foci at (0, ±7) is x^{2}/9 - y^{2}/40 = 1.

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