Question 753377
What is the asymptote equation for hyperbolas?
Standard form of equation for  hyperbolas: 
With horizontal transverse axis: {{{(x-h)^2/a^2-(y-k)^2/b^2=1}}}, (h,k)=(x,y) coordinates of center
With vertical transverse axis: {{{(y-k)^2/a^2-(x-h)^2/b^2=1}}}, (h,k)=(x,y) coordinates of center

Asymptote equations for hyperbolas are straight lines of the form: y=mx+b, m=slope, b=y-intercept.
These lines go thru the center of the hyperbola.
For hyperbolas with vertical transverse axis, slopes=ħa/b
For hyperbolas with horizontal transverse axis, slopes=ħb/a
Since you have a point on the line(center)and the slope, you can derive two straight line equations, one with a positive slope and the other with a negative slope