Thread: Curve defined by two implicit functions

The curve r(t) passing through the point is defined implicitly by the equations:

x^2y + y^2x + xyz + z^2 = 4
x + y + z = 3

i) Find the equation of the tangent line to this curve at the given point.
ii) Assume that we may choose x = t as the parameter. Find formulae for dy/dt and d^2y/dt^2.

I'm not sure how to tackle these questions. For i), can I use either of the two equations?

Well, if x=t, then what you are really looking for are the first and second derivatives of y with respect to x. Start by simplifying , and then substituting to get . Next differentiate implicitly to find : . Isolate and repeat the process to get . This should be enough to get you started.

Originally Posted by My Little Pony

The curve r(t) passing through the point is defined implicitly by the equations:

x^2y + y^2x + xyz + z^2 = 4
x + y + z = 3

i) Find the equation of the tangent line to this curve at the given point.
ii) Assume that we may choose x = t as the parameter. Find formulae for dy/dt and d^2y/dt^2.

I'm not sure how to tackle these questions. For i), can I use either of the two equations?

Didn't you already post this

http://www.mathhelpforum.com/math-he...ine-curve.html