Hyperbolas Page 4

Page 4

Examples and Practice Questions on Sketching Hyperbola

Let's review two examples we've seen earlier.

Example 1 on page 2 of this module:
x²/ 4 - y²/ 9 = 1 Example 2 on page 2:
-x²/ 3 + y²/ 4 = 1

Distance between the vertices:
2a = 2(2) = 4 units Distance between the vertices:
2b = 2(2) = 4 units

Slopes of the asymptotes:
+b/a = 3/2 and -b/a = -3/2. Slopes of the asymptotes:
+b/a = 2/Ö3 and -b/a = -2/Ö3

Knowing the vertices and the slopes of the asymptotes helps us to define the width of the branches of the hyperbola.

In the following questions you will use the standard equation of a hyperbola centred at the origin to describe and sketch the graph of a hyperbola.

x² - y² = 1 and - x² + y² = 1

a² b² a² b²

Let's review two examples we've seen earlier.
Example 1 on page 2 of this module: x²/ 4 - y²/ 9 = 1	Example 2 on page 2: -x²/ 3 + y²/ 4 = 1

Distance between the vertices: 2a = 2(2) = 4 units	Distance between the vertices: 2b = 2(2) = 4 units
Slopes of the asymptotes: +b/a = 3/2 and -b/a = -3/2.	Slopes of the asymptotes: +b/a = 2/Ö3 and -b/a = -2/Ö3
Knowing the vertices and the slopes of the asymptotes helps us to define the width of the branches of the hyperbola.
In the following questions you will use the standard equation of a hyperbola centred at the origin to describe and sketch the graph of a hyperbola.