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/a² - (y - k)²/b² = 1

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

Distance from center to vertices

a = 9 ⇒ a² = 81

Distance from center to vertices which is given from the foci

c = 10

⇒ c² = 100

Using the Pythagorean formula,

c² = a² + b²

Substituting the values

100 = 81 + b²

So we get,

b² = 100 - 81 = 19

Substituting the values in the standard form

x²/81 - y²/19 = 1

Therefore, the equation of the hyperbola is x²/81 - y²/19 = 1.

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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 x²/81 - y²/19 = 1.