Solve the problem.
-Find an equation for the level curve of the function $\mathrm { f } ( \mathrm { x } , \mathrm { y } ) = 16 - \mathrm { x } ^ { 2 } - \mathrm { y } ^ { 2 }$ that passes through the point $( \sqrt { 2 } , \sqrt { 5 } )$.
A) $x ^ { 2 } + y ^ { 2 } = - 7$
B) $x ^ { 2 } - y ^ { 2 } = 7$
C) $x ^ { 2 } + y ^ { 2 } = 23$
D) $x ^ { 2 } + y ^ { 2 } = 7$

Question

Quizplus · Accepted Answer

The level curve is found by setting $f(x, y) = c$. At the point $(\sqrt{2}, \sqrt{5})$, $f(\sqrt{2}, \sqrt{5}) = 16 - (\sqrt{2})^2 - (\sqrt{5})^2 = 16 - 2 - 5 = 9$. So, the equation is $x^2 + y^2 = 7$.

Solve the Problem f(x,y)=16−x2−y2\mathrm { f } ( \mathrm { x } , \mathrm { y } ) = 16 - \mathrm { x } ^ { 2 } - \mathrm { y } ^ { 2 }f(x,y)=16−x2−y2

Solve the Problem $\mathrm { f } ( \mathrm { x } , \mathrm { y } ) = 16 - \mathrm { x } ^ { 2 } - \mathrm { y } ^ { 2 }$