Find an equation of the line tangent to 2x^2-x-ln(x-4)-y^2=9 at (5,6)
differentiate implicitly
4x - 1 - 1/(x-4) - 2ydy/dx = 0
plug in (5,6) to get the slope which is dy/dx
Now you are back to a simple grade 9 problem of finding the equation of a straight line given the slope and a point