If $Y = X ^ { 2 } + Z ^ { 2 }$ ,the contour lines.
A)are concentric circles.
B)are parabolas.
C)are hyperbolas.
D)intersect whenever either X or Z is zero.

Question

Quizplus · Accepted Answer

The equation $Y = X^2 + Z^2$ is the equation of a circular cone (with the apex at the origin). When this cone is intersected by a plane perpendicular to the Y-axis, the resulting intersection is a circle with radius $\sqrt{Y}$. So, the contour lines of the function $Y = X^2 + Z^2$ are just circles centered at the origin. Therefore, the correct choice is A, which states that the contour lines are concentric circles.

If Y=X2+Z2Y = X ^ { 2 } + Z ^ { 2 }Y=X2+Z2

If $Y = X ^ { 2 } + Z ^ { 2 }$