How do you find the standard form of the equation of the hyperbola given the properties vertices (10,5), asymptotes #y=+1/2(x6)+5#?
1 Answer
There are two standard forms:

#(x  h)^2/a^2 (yk)^2/b^2 = 1# 
#(y  k)^2/a^2 (xh)^2/b^2 = 1#
The pointslope form for the equations of the asymptotes is:
Therefore, the equations,
This information coupled with one of the vertices given to be,
Substitute 6 for h and 5 for k:
The point
Substitute the value of "a" into equation [1.1]:
The general form for the asymptotes of a hyperbola with a horizontal transverse axis is:
Again, using the equations,
Substitute 16 for "a" and solve for "b":
Substitute the value for "b" into equation [1.2]: