Working with the hyperbola; identifying similarities and differences; problem solving with an emphasis on working with the asymptotes.

1. The Standard Form for the Equation of a Hyperbola
Horizontal Orientation Vertical Orientation
Differences
Similarities
In the horizontal hyperbola the term containing
They are both equal to 1.
x is positive while for the vertical hyperbola
They are both over a2 and b2. the term containing x is negative.
The horizontal hyperbola has a2
They are both a difference of squares.
2 2 2
below (x-h) and b below (y-k)
They both show the center (h,k).
vice versa for the vertical hyperbola.
Both x and y are squared in each of the
equations.
They both subtract terms within the equation.
a is the length of the semi-transverse axis.
b is the length of the semi-conjugate axis.

2. Conics Animations Source

3. Conics Animations Source

4. Conics Animations Source

5. Conics Animations Source

6. For the hyperbola whose equation is given below.
(i) Write the equation in standard form
(ii) Determine the lengths of the transverse and conjugate axes, the
coordinates of the verticies and foci, and the equations of the asymptotes.
(iii) Sketch a graph of the hyperbola. SLOPE INTERCEPT FORM

7. For the hyperbola whose equation is given below.
(i) Write the equation in standard form
(ii) Determine the lengths of the transverse and conjugate axes, the
coordinates of the verticies and foci, and the equations of the asymptotes.
(iii) Sketch a graph of the hyperbola.

8. For the hyperbola whose equation is given below.
(i) Write the equation in standard form
(ii) Determine the lengths of the transverse and conjugate axes, the
coordinates of the verticies and foci, and the equations of the asymptotes.
(iii) Sketch a graph of the hyperbola.