# Tangent of Implicit differentiation

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?

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!)
• i got the sum as $-35/13$ is that correct? – user3467226 Oct 14 '14 at 4:12
• it's no hard calculations, but I want first to know how did you differentiate to obtain $\frac{dy}{dx}$? – chouaib Oct 14 '14 at 4:16
• @user3467226 how you got $24x^2-11y$ shouldn't it be $24x^2+11y$ ? – chouaib Oct 14 '14 at 4:27
• I am weak on minus signs, but $24x^2-11y$ looks OK. – André Nicolas Oct 14 '14 at 4:43
• @AndréNicolas, my bad !! don't know even how I managed to get the plus sign, btw I'm weaker when it comes to minus sign ;) – chouaib Oct 14 '14 at 4:50