# How do you find the center and vertices and sketch the hyperbola #4y^2-x^2=1#?

##### 1 Answer

Jan 31, 2017

See explanation and graph.

#### Explanation:

TIn the standard form the equation is

Center C is the origin (0, 0)

Major axis : y-axis, x = 0.

Transverse axis : x-axis, y = 0.

Semi major axis

Semi transverse axis

Eccentricity :

Vertices A and A' on major axis x = 0 :

Foci S and S' on major axis : (

The asymptotes :

The Socratic graph is inserted.

graph{(4y^2-x^2-1)(4y^2-x^2)((y-sqrt5)^2+x^2-.01)((y+sqrt5)^2+x^2-.01)((y-.5)^2+x^2-.01)((y+.5)^2+x^2-.01)=0 [-5, 5, -2.5, 2.5]}