SOLUTION: Find the equation of the hyperbola, in general form, with vertices (±2,3) and a conjugate axis that measures 12 units.

We plot the vertices (±2,3). Draw the transverse axis which is the line joining
them. Then draw the conjugate 12 units long so that the transverse axis and
conjugate axes are perpendicular bisectors of each other at the center, which
is (0,3).



We draw the defining rectangle so that the two axes bisect it:




We draw and extend the two diagonals of the defining rectangle, which are the
asymptotes of the hyperbola:



Now we sketch in the hyperbola:



The equation is



where a = half the transverse axis = 2
and b = half the conjugate axis = 6
and h = the x-coordinate of the center = 0
and k = the y-coordinate of the center = 3



Which simplifies to:



Edwin