Question

Find an equation of the tangent line to the hyperbola: x^(2)-2y^(2)=1 at the point (a,b).

Answer 1

find m= dy/dx at point (a,b) then use equation (y-b)=m(x-a)

Answer 2

I found the slope= a/2b is that right?

Answer 3

yes right

Answer 4

What would the equation be then?

Answer 5

equation of a straight line is y=mx+c
you know m put it in above eqn after that
by putting point (a,b) you will get c
so put c back in above equation you will get your final answer

Answer 6

Find an equation for the slope of the tangent line to the hyperbola: x^(2)-2y^(2)=1 by differentiating both sides with respect to x, and then solving the resulting equation for (dy/dx). That will be the formula for the slope of your tangent line. Remember that y is assumed to be a function of x here, so you'll need to use the chain rule in finding that derivative.