# Find an equation in standard form for the hyperbola with vertices at (0, ± 2) and foci at (0, ± 11).

**Solution:**

A hyperbola is an open curve with two branches, the intersection of a plane with both halves of a double cone.

The centre bisects the line joining the vertices (0, -2) and (0, 2)

C is the origin

Distance between the vertices is the transverse axis 2a = 4

⇒ a = 2

Distance between foci = 2a × eccentricity

So,

4e = 18

⇒ e = 9/2

Semi transverse axis b = a√(e^{2} - 1)

Substituting the values

b = 2√(81/4 - 1)

b = √77

a^{2} = 4 and b^{2} = 77

So the equation of the hyperbola is x^{2}/4 - y^{2}/77 = 1

## Find an equation in standard form for the hyperbola with vertices at (0, ±2) and foci at (0, ±11).

**Summary:**

An equation in standard form for the hyperbola with vertices at (0, ±2) and foci at (0, ±11) is x^{2}/4 - y^{2}/77 = 1.

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