Identify the trace of the surface $x = y ^ { 2 } + z ^ { 2 }$ in the plane x = y.
A)ellipse but not a circle
B)parabola
C)hyperbola
D)circle
E)two parallel straight lines
F)two intersecting straight lines
G)point
H)straight line

Question

Quizplus · Accepted Answer

The trace of the surface $x = y ^ { 2 } + z ^ { 2 }$ in the plane x = y is a circle. This is because the equation of the surface in the plane x = y is $y ^ { 2 } + z ^ { 2 } = y$, which is the equation of a circle with radius 1 and center at the origin.

Identify the Trace of the Surface x=y2+z2x = y ^ { 2 } + z ^ { 2 }x=y2+z2

Identify the Trace of the Surface $x = y ^ { 2 } + z ^ { 2 }$