Find the equation for the level surface of the function through the given point.
-$$f ( x , y , z ) = \frac { x ^ { 2 } y } { x z + y ^ { 2 } } , ( 2,7,8 )$$
A) $\frac { 28 } { 65 } = \frac { x ^ { 2 } y } { x z + y ^ { 2 } }$
B) $65 \left( x z + y ^ { 2 } \right) = 28 x ^ { 2 } y$
C) $\frac { 14 } { 39 } = \frac { x ^ { 2 } y } { x z + y ^ { 2 } }$
D) $\frac { 14 } { 65 } = \frac { \mathrm { x } ^ { 2 } \mathrm { y } } { \mathrm { xz } + \mathrm { y } ^ { 2 } }$

Question

Quizplus · Accepted Answer

To find the equation of the level surface of the function through the point (2,7,8), we substitute these values into the function: $$f(2,7,8) = \frac{2^2 \cdot 7}{2 \cdot 8 + 7^2} = \frac{28}{16 + 49} = \frac{28}{65}$$. Thus, the equation of the level surface is $\frac{28}{65} = \frac{x^2y}{xz + y^2}$.

Find the Equation for the Level Surface of the Function f(x,y,z)=x2yxz+y2,(2,7,8)f ( x , y , z ) = \frac { x ^ { 2 } y } { x z + y ^ { 2 } } , ( 2,7,8 )f(x,y,z)=xz+y2x2y​,(2,7,8)

Find the Equation for the Level Surface of the Function $f ( x , y , z ) = \frac { x ^ { 2 } y } { x z + y ^ { 2 } } , ( 2,7,8 )$