Question

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin.

Vertices:  (0, ±2);    foci:  (0, ±4)

Answer 1

Step 1:

The vertices are and foci is .

Observe vertices and foci, coordinates are equal.

So, the hyperbola has a vertical transverse axis and its standard form of the equation is

.

Where,

is the center.

The distance between center and vertex is .

The distance between center and focus is .

.

Using midpoint formula, the center of the hyperbola is .

The distance between center and vertex is .

The distance between center and focus is .

 Substitute the values of  in standard form of a equation.

Solution :

The standard form of the hyperbola is .