Write the equation for the tangent line in slope intersect form.
48(x^2+y^2)^2 =625xy^2

Question

Write the equation for the tangent line  in slope intersect form. 
48(x^2+y^2)^2 =625xy^2

mathteacher1729 · Answer

Tangent LINE or tangent PLANE? Also, at what point?

anonymous · Answer

tangent line:)

anonymous · Answer

(3,4)

mathteacher1729 · Answer

Take dy/dx (implicit differentiation with respect to x) of both sides, and solve for dy/dx.  Then input (3,4) into that and you'll have the slope at that point.

anonymous · Answer

can you show me how that would be done?

mathteacher1729 · Answer

It's a bit much to type. Basically it's implicit differentiation. More on that here: http://tutorial.math.lamar.edu/Classes/CalcI/ImplicitDiff.aspx Nice videos if it here: http://patrickjmt.com/#calculus (do edit > search for "implicit" to find it on the page). If you go to http://www.wolframalpha.com and type d/dx (48(x^2+y^2)^2 =625xy^2) then click "show steps" it will give you all the gory details.