Answer:
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
