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### UNIT 9  : THE CONICS

LESSON 5:  THE HYPERBOLA

Definition:   Given two fixed points in the plane F1 and F2.  A hyperbola is the locus (set) of points P such that the difference |PF2 – PF1 |  is a constant.  The two fixed points are the foci.

The centre is the midpoint of the line segment joining the two foci (F1F2).

Hyperbola with foci on the x-axis:

Hyperbola with foci on the y-axis:

Example 1:

Solution:

Example 2:

Given the hyperbola with equation 9x2 - 4y2 = - 36.

a) Put the equation in standard form and find the

values of a, b, c, e.

b) Determine the coordinates of the vertices.

c) State the length of the transverse and conjugate axes.

d) Find the equations of the asymptotes.

e) Draw the graph.

Example 3:

Solution:

Example 4:

Given the hyperbola with equation 9x2 –54x – 25y2 + 200y – 544 = 0.

a) Put the equation in standard form and find the

values of a, b, c, e.

b) Determine the coordinates of the vertices.

c) State the length of the transverse and conjugate axes.

d) Find the equations of the asymptotes.

e) Draw the graph