The focal points of a hyperbola are (0,6) and (0,-6), and the point (5,6) is on one of its branches. Find coordinates for the points where the hyperbola intersects its major axis. Also find equations for the asymptotes, and use them to help you draw the curve.

Answer 1

the center is clearly at (0,0) so the equation is

y^2/a^2 - x^2/b^2 = 1
with c=6, so a^2+b^2 = 36
The given point says that
36/a^2 - 25/b^2 = 1
36/a^2 - 25/(36-a^2) = 1
a = 4 or 9
clearly a cannot be 9, so a=4 and b^2 = 20
Thus, the equation of the hyperbola is

y^2/16 - x^2/20 = 1
and the rest you can easily determine, right?