Identify the trace of the surface $x = 2 y ^ { 2 } + 3 z ^ { 2 }$ in the plane x = 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

The trace of the surface $x = 2 y ^ { 2 } + 3 z ^ { 2 }$ in the plane $x = 1$ is obtained by substituting $x = 1$ into the equation, yielding $1 = 2 y ^ { 2 } + 3 z ^ { 2 }$. This equation represents an ellipse because it is a quadratic equation in $y$ and $z$ with positive coefficients, but it does not satisfy the condition for a circle since the coefficients of $y^2$ and $z^2$ are not equal.

Identify the Trace of the Surface x=2y2+3z2x = 2 y ^ { 2 } + 3 z ^ { 2 }x=2y2+3z2

Identify the Trace of the Surface $x = 2 y ^ { 2 } + 3 z ^ { 2 }$