Homework Help

# 1a) Sketch and identify the surface `4y^2-x^2-(z-2)^2=4` ` ` b)Find a vector function...

eNoter

• Up
• 0
• Down

1a) Sketch and identify the surface

`4y^2-x^2-(z-2)^2=4`

` `

b)Find a vector function that represents the curve of intersection of the surfaces `x^2+y^2=8and z=3xy+7`

``

Posted by haqc on October 22, 2013 at 6:14 AM via web and tagged with math

High School Teacher

Valedictorian

• Up
• 0
• Down

Let us assume

`x=m`  then

`m^2+y^2=8`

`y^2=8-m^2`

`y=+-sqrt(8-m^2)`                 (i)

Substitute x and y in the equation of the curve  z=3xy+7 i.e.

`z=3msqrt(8-m^2)+7 and z=-3msqrt(8-m^2)+7`

Thus vector functions are

`(m,sqrt(8-m^2),3msqrt(8-m^2)) and (m,-sqrt(8-m^2),-3msqrt(8-m^2)+7) .`

Posted by aruv on October 22, 2013 at 8:23 AM (Answer #1)

High School Teacher

(Level 3) Associate Educator

• Up
• 0
• Down

a)

As you can see from the picture below this hyperboloid of two sheets. This is easily seen even without picture because general formula for hyperboloid with two sheets is

`x^2/a^2-y^2/b^2-z^2/c^2=1`

where `a,b,c in RR`  ``

Images:
This image has been Flagged as inappropriate Click to unflag
Image (1 of 1)

Posted by tiburtius on October 22, 2013 at 12:55 PM (Answer #2)