# level curves

• May 24th 2008, 10:11 PM
mathshelpbook
level curves
for f(x,y) = 1 -2x^2 - 3y^2
just wondering if someone could please help me find the equation of the curve of intersection of the surface z=f(x,y) with the plane x=1
i can sketch the levelcurves for valuesof c and sketch the cross sections of the surface in the xz and yz planes, will that help?
i couldn't find an example of how to do this type of question in my notes or textbook, so any help would be much appreciated!
• May 25th 2008, 12:30 AM
earboth
Quote:

Originally Posted by mathshelpbook
for f(x,y) = 1 -2x^2 - 3y^2
just wondering if someone could please help me find the equation of the curve of intersection of the surface z=f(x,y) with the plane x=1
i can sketch the levelcurves for valuesof c and sketch the cross sections of the surface in the xz and yz planes, will that help?
i couldn't find an example of how to do this type of question in my notes or textbook, so any help would be much appreciated!

1. The graph of f is a paraboloid

2. The intersection of the paraboloid with a plane parallel to the axis of the paraboloid must be a parabola.

3. Use parametric equation to get the intersection parabola:

$\displaystyle \left|\begin{array}{l}x=1 \\ y=t \\z=-1-3t^2\end{array}\right.$

4. I've attached a drawing of f and the cutting plane. Because it is very difficult to detect the parabola in this drawing I've sketched the parabola alone in a separate coordinate system.