Find the equations of xy, xz, yz traces?

Question

x=4-4y²-z²

Find the equations of xy traces? Chose one and fill in the blank if you have to

1. Trace is not a single point the equation of the xy-trace is __________
2. The trace is a single point (_, _, _)
3. There is no xy -trace

Find the equations of xz traces? Chose one fill in the black if you have to

1. Trace is not a single point the equation of the xy-trace is __________
2. The trace is a single point (_, _, _)
3. There is no xz -trace

Find the equations of yz traces? Chose one fill in the blank if you have to

1. Trace is not a single point the equation of the xy-trace is __________
2. The trace is a single point (_, _, _)
3. There is no yz -trace

Answer 1

Given equation: x = 4 - 4y² - z²;

To get xy trace we set z = 0, we get x = 4 - 4y², which is parabola, but not a single point

To get xz trace we set y = 0, we get x = 4 - z², which is parabola, but not a single point;

To get yz trace we set x = 0, we get 4y² + z² = 4, which is ellipse, but not a single point.

Answer 2

Given equation: x = 4 - 4y² - z²;

To get xy trace we set z = 0, we get x = 4 - 4y², which is parabola, but not a single point

To get xz trace we set y = 0, we get x = 4 - z², which is parabola, but not a single point;

To get yz trace we set x = 0, we get 4y² + z² = 4, which is ellipse, but not a single point.