Thread: Line-Surface intersection

Find the coordinates of the point(s) of intersection of the line x = 1 - t, y = 2 + 3t, z = 1 - t and the surface z = x^2 + 2y^2.

Im completely lost. My book has not example of this and I dont remember seeing a problem like this.

Originally Posted by kenshinofkin

Find the coordinates of the point(s) of intersection of the line x = 1 - t, y = 2 + 3t, z = 1 - t and the surface z = x^2 + 2y^2.

Im completely lost. My book has not example of this and I dont remember seeing a problem like this.

are you sure taht you have this copied correctly?

Hello, kenshinofkin!

I agree with Mathstud28 . . . The problem has no solution.

Find the coordinates of the point(s) of intersection of the line: .
. . and the surface: .

The usual way is to substitute the parametric equations into the surface's equation.

Then we have: .

. . . . . . . . .


But this simplifies to: . . . . which has no real solutions.

. . The line does not intersect the elliptic paraboloid.

hmm my teacher gave it to us. Maybe its wrong.