Thread: Graph of a Multivariable Equation

1. Graph of a Multivariable Equation

I have two questions here. Here is the first one.

The given equation is:

$4 = (x-1)^2 + (y+3)^2 + (z-2)^2$

Are there any equations of the circles where the sphere defined by the above equation that intersect the coordinate planes (xy, xz, and yz) as well as any points where the sphere intersects each coordinate axis.

I am not quite too sure where to begin, should I simply pick one variable, say x, and make y and z zero then solve? I am a fair bit lost already.

The second problem is:

By setting one variable constant find a plane that intersects the graph of:

$z = (x^2 + 1)siny + xy^2$

in a parabola, straight line and sine curve.

For the parabola, would it be as simple as setting $y = \frac {\pi} {2}$ and the sine curve is as easy as setting $x = 0$ and I am not sure how to form a straight line by setting one variable constant.

Thanks for the help ahead of time.

2. 1) Note that that equation is not a sphere because one of the exponents is 3. Is that a typo? If it were a sphere, you could indeed find its intersection with the (say) x-axis by setting y=z=0. Similarly, you could find its intersection with the xy plane by setting z=0.

2) y=0.

3. Thanks for that, and yes, it was a typo, sorry about that, I am going to fix it now, but thank you, I appreciate it.