Find an equation for the level curve of the function f (x, y) that passes through the given point. f (x, y) = 64 - 4x2 - 4y2, (3 underroot 2, 3 underroot 2)  

the level curve of the function that passes through the point is x² - y² = - 36

Step-by-step explanation:

Given that;

the function is;

f(x, y) = 64 - 4x² - 4y²

At the point P = ( 3√2, 3√2)

so we have

f( 3√2, 3√2) = 64 - 4(3√2)² - 4(3√2)²

= 64 - 72 - 72 = -80

so the level curve containing the point P = ( 3√2, 3√2) is the curve,

f(x,y) = -80

64 - 4x² - 4y² = -80

divide through by 4

4x² - 4y² = -80 - 64

4x² - 4y² = 144

divide through by 4

x² - y² = - 36

therefore, the level curve of the function that passes through the point is,

x² - y² = - 36

step-by-step explanation:

just plug in each number for x and see which ones work and don't