PRACTICE
PROBLEMS:
1.
Find the equation of the hyperbola with an eccentricity of
,^{ }directrices
, and
foci at
2.
Find the equation of the hyperbola with an eccentricity of 5/3, foci at ( ±
5,0), and directrices x = ± 9/5.
Find
the foci, directrices, eccentricity, equations of the asymptotes, and length of
the focal chord of the hyperbolas given in problems 3 and 4.
ANSWERS:
^{}
The hyperbola can be represented by an equation in the
general form
Ax^{e}+Cy^{2}+Dx+Ey+F=0
where the capital letters refer to independent constants
and A and C have different signs. These equations can be reduced to standard
form in the same manner in which similar equations for the ellipse were reduced
to standard form. The standard forms with the center at (h,k) are given by the
equations
and
