Describe the level curves of the function $f ( x , y ) = x ^ { 2 } + y ^ { 2 } + 3 x - 4 y + 73$ .
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 function $f(x, y) = x^2 + y^2 + 3x - 4y + 73$ represents concentric circles when rewritten in the form $(x - h)^2 + (y - k)^2 = r^2$, indicating circles with the same center but different radii.

Describe the Level Curves of the Function f(x,y)=x2+y2+3x−4y+73f ( x , y ) = x ^ { 2 } + y ^ { 2 } + 3 x - 4 y + 73f(x,y)=x2+y2+3x−4y+73

Describe the Level Curves of the Function $f ( x , y ) = x ^ { 2 } + y ^ { 2 } + 3 x - 4 y + 73$