Let $f ( x , y ) = x ^ { 2 } - y ^ { 2 }$ . Then the level curve for z = 3 is

A)A circle
B)An ellipse
C)A hyperbola
D)A cardioid
E)A limaçon

Name: Let $f ( x , y ) = x ^ { 2 } - y ^ { 2 }$ . Then the level curve for z = 3 is A)A circle B)An ellipse C)A hyperbola D)A cardioid E)A limaçon
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Question

Let $f ( x , y ) = x ^ { 2 } - y ^ { 2 }$ . Then the level curve for z = 3 is

A)A circle
B)An ellipse
C)A hyperbola
D)A cardioid
E)A limaçon

Quizplus · Accepted Answer

The equation for the level curve is obtained by setting $f(x, y) = 3$, which gives $x^2 - y^2 = 3$. This is the equation of a hyperbola, not a circle, ellipse, cardioid, or limaçon.

Let f(x,y)=x2−y2f ( x , y ) = x ^ { 2 } - y ^ { 2 }f(x,y)=x2−y2

Let $f ( x , y ) = x ^ { 2 } - y ^ { 2 }$