is the equation of a hyperbola like this " )( "

with center (h,k), semi-transverse axis = a, semi-conjugate axis = b

  

  

We 

1. Plot the center (2,3).
2. Draw the transverse axis (red) of 2a = 2(6) = 12
3. Draw the conjugate axis (blue) of 2b = 2(5) = 10,
4. defining rectangle (in green)
5. Draw and extend diagonals forming asymptotes (dotted lines),
6. Sketch the hyperbola.
7. Calculate c by c²=a²+b²=36+25=61, c=
8. Foci are (h±c,k) which are (2-,3), (2+,3), the big black dots.
9. Find equations of asymptotes.  Slopes are  through (h,k)
                                  Slopes are (((""+-5/6}}} through (2,3)

Use point-slope formula:
y - y1 = m(x - x1)
where (x1,y1) = (2,3)
 
y - 3 = (x - 2)  and  y - 3 = (x - 2)

You can simplify those equations.







Edwin