# Math Help - line-surface intersection

1. ## line-surface intersection

I'm trying to figure out how to find the intersection of a line and a surface in 3-space. For example, what if I had the equation for a line in parametric form:

x = 1 + t
y = -2 + t
z = 1 - 2t

and a surface (of an ellipsoid) in parametric form:

x = 2*cos(u)*cos(v)
y = 2*cos(u)*sin(v)
z = sin(u)

where -pi/2<u<pi/2 and -pi<v<pi

How would I go about finding the intersection point?

2. ## Re: line-surface intersection

Verify that $x^2+y^2+4z^2=4$ and solve the quadratic equation $(1-t)^2+(-2+t)^2+4(1-2t)^2=4.$