Solving the Equation 3x^2+8xy-3y^2=1 - What's Next?

[BlackJack]

I have a questions:

Given is the equation 3x^2 +8xy-3y^2 = 1
I know have to find the function x -> y:=f(x) which is implicit defined by the equation above.
I have solved the question for x1,x2 = (4x+/- sqr(25x^2+3)) / 3

My question what do I have to do now?

-----------------------------------------

 

[marlon]

I am sorry but don't you need to look for $$\frac {dy}{dx}$$ first by differentiating your given equation ?

This would be something like $$6xdx + 8 (xdy + ydx) - 6ydy = 0$$ Then solve for $$\frac {dy}{dx}$$.

marlon