Describe the level curves of the function $f ( x , y ) = \sqrt { x ^ { 2 } + ( y - 1 ) ^ { 2 } } - y$ .
A)Concentric circles
B)Non-concentric circles
C)Concentric ellipses (not circles)
D)Non-concentric ellipses (not circles)
E)Parabolas with the same vertex
F)Parabolas with the same focus
G)Hyperbolas with the same vertices
H)Hyperbolas with the same foci

Question

Quizplus · Accepted Answer

The level curves of the function are parabolas with the same focus, as the function represents the distance from a point minus the y-coordinate, which is a characteristic of parabolas.

Describe the Level Curves of the Function f(x,y)=x2+(y−1)2−yf ( x , y ) = \sqrt { x ^ { 2 } + ( y - 1 ) ^ { 2 } } - yf(x,y)=x2+(y−1)2​−y

Describe the Level Curves of the Function $f ( x , y ) = \sqrt { x ^ { 2 } + ( y - 1 ) ^ { 2 } } - y$