Question

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

Vertices: (0, 4), (0, 0);

passes through the point  (√5, - 1)

Answer 1

Step 1:

The vertices are and point is .

Observe vertices, coordinates are equal.

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 a.

The distance between center and focus is c.

.

Using midpoint formula, the center of the hyperbola is 

The distance between center and vertex is .

Step 2:

Find b, by using hyperbola equation passing through point .

Substitute in .

Step 3:

Substitute , in .

The hyperbola equation is

Solution :

The hyperbola equation is