12.3 Hyperbolas

The Anatomy of the Hyperbola

For each ellipse whose equation is given below(i) Write the equation in standard form(ii) Determine the lengths of the major and minor axes, the

coordinates of the verticies, and the coordinates of the foci.(iii) Sketch a graph of the ellipse.

The Standard Form for the Equation of a Hyperbola

Horizontal Orientation Vertical Orientation

Similarities Differences

• have the same terms• both equal 1• both are differences• both have same denominators• both have square binomials• (h, k) indicates center

• numerators have different orientation• numerators have opposite signs