The following link will launch a video in a new window/tab, which will show how to graph a hyperbola. When you are finished watching the video, close the window/tab to return to this lesson.

Graphing the Equation of a Hyperbola

The steps to graphing a hyperbola are a little different from graphing a circle or an ellipse:

Using this equation of a hyperbola as our example, follow the steps:

x minus one squared over 25
(*x* − *1*)^{2}
25
−
y plus three squared over sixteen
(*y* + *3*)^{2}
16
= 1

- Find the coordinates of the center point (
*h, k*) and plot.

- Determine the length of the
*major axis*and the*minor axis*by taking the square root of the numbers in the denominators of each term in the equation.

- Determine the direction the hyperbola opens based on which term is positive.

- Mark points along the horizontal (
*major axis*) and vertical (*minor axis*) lines through the center point that are the indicated radial distance from the center in each direction.

Sketch a rectangle, including each of the previously plotted points at the centers of each of the sides of the rectangle.

Vertices of the rectangle will be the intersections of the vertical and horizontal lines through the plotted points.

Draw in the asymptotes through the diagonals of the rectangle.

What are the slopes of the asymptotes?

The points on the rectangle through the major axis are the vertices of the curves of the hyperbola. (in this case, (-4, -3) and (6, -3). Sketch the curves from the vertices and approaching the asymptotes.