Tangent Line Equation for Ellipse: Parametric Equations at (1,2,2)

[mattibo]

Homework Statement

The ellipsoid 4x^2 + 2y^2 + z^2 = 16 intersects the plane y = 2 in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1,2,2)

Homework Equations

x = x0 + at
y = y0 + bt
z = z0 + ct

The Attempt at a Solution

Well i know that x0,y0 and z0 are given by the point(1,2,2) and that's pretty much it. I don't know how to use the information given in the first part of the question.
I put y=2 in the ellipsoid equation and got 4x^2 + z^2 = 8. Now what?

 

[HallsofIvy]

Homework Statement

The ellipsoid 4x^2 + 2y^2 + z^2 = 16 intersects the plane y = 2 in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1,2,2)

Homework Equations

x = x0 + at
y = y0 + bt
z = z0 + ct

The Attempt at a Solution

Well i know that x0,y0 and z0 are given by the point(1,2,2) and that's pretty much it. I don't know how to use the information given in the first part of the question.
I put y=2 in the ellipsoid equation and got 4x^2 + z^2 = 8. Now what?

Great! Now find a tangent line to that ellipse at x= 1, z= 2. What that will give you will probably be something line z= ax+ b. Okay, let x= t, the parameter. x= t, z= at+ b and, of course, y= 2.