# Thread: Equations for the tangent line to the curve

1. ## Equations for the tangent line to the curve

Find equations for the tangent line to the curve

$xyz + z^{3} = 24, x^{3}y^{2}z + y^{3} = 4x - 2$

at the point (1,-1,3)

Okay, if I can find parametric equations representing this curve I can easily find a tangent vector along the curve at the point (1,-1,3) by simply differentiating my parametric equations.

At this point I'll have a tangent vector along the curve, I want a tangent line to the curve at the point (1,-1,3), so I'll simply define a new line that points in the direction of my tangent vector, starting at the point (1,-1,3).

Problem is, I can't seem to find a reasonable way of finding parametric equations for the curve.

Any ideas?

EDIT: I've solved it by taking the gradient of both functions F(x,y,z) = 0 and G(x,y,z) = 0 evaluated at the point (1,-1,3) and taking the cross product between to produce my vector along the tangent line.