Chapter 10.1, Problem 94E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Find the minimum value of ( u − v ) 2 + ( 2 − u 2 − 9 v ) 2 for 0 < u < 2 and v > 0 .

To determine

To Calculate: The least value of the equation (uv)2+(2u29v)2.

Explanation

Given: The equation (uâˆ’v)2+(2âˆ’u2âˆ’9v)2, where 0<u<2 and v>0.

Formula Used:

Distance formula is given as, D=(x2âˆ’x1)2+(y2âˆ’y1)2

Calculation:

Consider a circle x2+y2=(2)2..........(1)

Assume, x=u, this implies y=2âˆ’u, such that the point (u,2âˆ’u) lies on the circle.

Also, consider a hyperbola given by y=9x

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