Level curve of function that passes through given point

$\begingroup$

I have a function $f(x,y)= 16-x^2-y^2$ that passes through the point $(2\sqrt(2),\sqrt(2))$ . How do I find out the equation of level curve? I dont have any idea . Pls provide hints.

What I am doing is putting the values in the function which gives $f(x,y)$ as $6$. So my level curve (I am not sure) should be

$6=16-x^2-y^2$Which gives $x^2+y^2=10$Which is wrong

$\endgroup$ 1

1 Answer

$\begingroup$

Plug the coordinates of the point in your function to get $f(x,y)=6$

Thus the level curve is $$16-x^2-y^2=6$$ Or $$x^2+y^2=10$$ which is a circle centered at the origin with radius $R=\sqrt {10}$

$\endgroup$ 2

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy