Determine the y-intercept(s) of the level curve, where f(x,y)=2e^(2sqrt(x^2+y^2)) and z=4.

suchonosdy 2022-07-23 Answered
Determine the y-intercept(s) of the level curve, where f ( x , y ) = 2 e 2 x 2 + y 2 and z = 4.
I started but setting 4 = f ( x , y ) then I solved for y and got 2 l n ( 2 ) 4 x 2 and I tried solving for y = 0. Is there a similar way to do this?
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Answers (1)

Kitamiliseakekw
Answered 2022-07-24 Author has 23 answers
So if z = 4, f ( x , y ) = 4.
Hence forth, 4 = 2 e 2 x 2 + y 2 . So yes, you were correct to this.
To find the y-intercepts, x = 0 since the intercepts are solely on the y-axis and you already know that z = 4.
You now have 4 = 2 e 2 y 2 for x = 0 , z = 4.
You cannot solve for the intercepts if y = 0 because you would be finding the x-intercepts instead!
Now, you can solve for y
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