Question

Find the standard form of the equation of the hyperbola with the given characteristics.

Vertices: (4, 1), (4, 9);    foci: (4, 0),  (4, 10)

Answer 1

Step 1:

The vertices are and foci are .

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.

  is the distance between center and vertex.

  is the distance between center and focus.

.

By the 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 the equation.

Solution :

The standard form of the hyperbola .