What's the equation of a generic hyperbola: x^2/a^2 - y^2/b^2 = 1 reflected across generic line: y = mx + b ?

Thanks:
Dufushypster

Do a transformation to make mx+b the ordinate, then change x' to -x', then rotate back to original reference frame.

By transformation, do you mean substitute mx+b for x in the hyperbola equation? Then I get lost about why change x' to -x' and the concept of "rotat[ing] back" is beyond my background in math. I think I need to see all the individual steps.

Thanks

I assumed that by reflecting you mean finding an equation for a mirror image of your curve with respect to y=mx+b. In general, rotation-reflection-rotation would do. In your case, hyperbola is symmetric wrt ordinate, so rotate your hyperbola by 2*alpha around intersection of Oy an y=mx+b, where alpha is the angle between Oy and y=mx+b. Look up tranformations: translation and rotation.