# Find the points on the surface z^2 = xy + 1 that are closest to the origin.

## Question:

Find the points on the surface {eq}z^2 = xy + 1 {/eq} that are closest to the origin.

## Shortest distance:

To find the closest distance the distance between the point and the surface with the help of distance formula {eq}d = \sqrt {{{\left( {x - {x_0}} \right)}^2} + {{\left( {y - {y_0}} \right)}^2} + {{\left( {z - {z_0}} \right)}^2}} {/eq} between two points {eq}\left( {x,y,z} \right), \left( {0,0,0} \right) {/eq}. Using the Second Derivative Test, {eq}D\left( {a,b} \right) = {f_{xx}}\left( {a,b} \right){f_{yy}}\left( {a,b} \right) - {\left[ {{f_{xy}}\left( {a,b} \right)} \right]^2} {/eq}

## Answer and Explanation:

Using the distance formula, you have {eq}d = \sqrt {{{\left( {x - {x_0}} \right)}^2} + {{\left( {y - {y_0}} \right)}^2} + {{\left( {z - {z_0}}...

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from High School Algebra I: Homework Help Resource

Chapter 23 / Lesson 16