Find the minimum value of $f ( x , y ) = x ^ { 2 } + y ^ { 2 } - 4 y + 4$ on the hyperbola $x ^ { 2 } - y ^ { 2 } = 4$
A) No minimum, unbounded below
B) 6
C) $12 \sqrt { 3 }$
D) 43

Name: Find the minimum value of $f ( x , y ) = x ^ { 2 } + y ^ { 2 } - 4 y + 4$ on the hyperbola $x ^ { 2 } - y ^ { 2 } = 4$ A) No minimum, unbounded below B) 6 C) $12 \sqrt { 3 }$ D) 43
Brand: Quizplus
Rating: 4.8 (27 reviews)

Question

Quizplus · Accepted Answer

To find the minimum value, substitute $y = \sqrt{x^2 - 4}$ into $f(x, y)$ and minimize the resulting expression. The minimum value is 6.

Find the Minimum Value Of f(x,y)=x2+y2−4y+4f ( x , y ) = x ^ { 2 } + y ^ { 2 } - 4 y + 4f(x,y)=x2+y2−4y+4

Find the Minimum Value Of $f ( x , y ) = x ^ { 2 } + y ^ { 2 } - 4 y + 4$