Tangent of Implicit differentiation

Question

So the question is $y^2 +11xy-8x^3=-700$ find two lines tangent to the curve at the points on the curve where x=5. What is the sum of their slopes?

i got $\frac{dy}{dx}=\frac{24x^2-11y}{11x+2y}$ but how do i get the sum of their slopes at x=5?

Answer 1

setting $x=5$ and solving the equation you will end up with two possible solutions for $y$:

$y=5$ and $y=60$

Now apply those two points to your differential equation to find the tangents $(5, 5)$ and $(5, 60)$ (assuming you differentiated correctly!)