Identify the trace of the surface $x ^ { 2 } = y ^ { 2 } + z ^ { 2 }$ in the plane y = 1.
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

When $y = 1$, the equation becomes $x^2 = 1 + z^2$, which is the equation of a hyperbola in the x-z plane.

Identify the Trace of the Surface x2=y2+z2x ^ { 2 } = y ^ { 2 } + z ^ { 2 }x2=y2+z2

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