Question

can someone answer this quadric surface using completing the square ?thank you :)

x^2 + 4y^2 - z^2 - 6x + 8y + 4z = 0

Answer 1

get your like variables together and complete the squares .... which part is giving you pause?

Answer 2

you can pull it apart into 3 quads if you like .... that might be less data to cull thru.

Answer 3

i don't know how to solve this..i'm sorry

Answer 4

do you know how to complete a square?

Answer 5

it means that it will have a two factors in each variables..all in all it has a 6 factors?

Answer 6

it is x^2 - 6x , 4y^2 + 8y and z^2 + 4z?

Answer 7

lets go ahead and split this up into 3 different parts:

x^2 + 4y^2 - z^2 - 6x + 8y + 4z = 0


x^2 -6x

4y^2 +8y

-z^2 + 4z

now that its organized better, you just work each one in its own right .... complete the square for each part

Answer 8

the key is, do you know how to complete a square? :)

Answer 9

ah.. its -z^2..

Answer 10

i'm sorry i forgot how to complete a square..

Answer 11

basically, you add and subtract a useful form of zero.

square half the "x" term ..... for example:

x^2 -6x ; the x term is -6, -6/2 = -3, (-3)^2 = 9. Lets add and subtract 9

x^2 -6x + 9 - 9; and condense the square

(x-3)^2 - 9

Answer 12

z will be trick only in that you have to account for the -

Answer 13

x^2 -6x ; the x term is -6, how it become -6/2?

Answer 14

we are trying to make a complete square, a perfect square.

numbers of the form (a+b)^2 are perfect squares: (2+5)^2 = 49, (3+1)^2 = 16, ...

we want to condense this thing back into some (a + b)^2 form, thats all. In order to do that we have to modify its form, but not its value. Since adding zero changes nothing ... its useful to us. BUT what form of zero?

lets expand

(a+b)^2 = a^2 +2ab + b^2 ; let a=x

(x+b)^2 = x^2 +2bx + b^2 notice that the b^2 is missing above. and we know that the "x" term in the middle is equal to 2b.

2b = -6

b = -6/2 = -3

b^2 = 9

Answer 15

so, adding and subtract 9; 9-9 = 0 right? will allow us to "complete" the square and alter its form ... not its value

Answer 16

4y^2 +8y

2b = 8

b = 8/2 = 4

b^2 = 16, +16-16 = 0

4y^2 +8y + (16-16)

therefore

4y^2 +8y = (2y +4)^2 - 16

Answer 17

oh..i see. thanks i will solve this..

Answer 18

btw do you know about contour plotting?

Answer 19

i would need a little more information to see if i have contour plotting rolling around in my head someplace :)

Answer 20

do you know what kind of contour plot is this if f(x,y) = \[\sqrt{x^2 + y^2}\] ?

Answer 21

so the height, or z, is dependent on x and y inputs

if we hold one input constant, we can generate a cross section plot and such, are some ideas ive got

z = sqrt(x^2+y^2)

z^2 = x^2 + y^2 is a circle, and so im gonna extrapolate that this is a sphere or hemisphere as a guess

Answer 22

http://web.monroecc.edu/manila/webfiles/calcnsf/javacode/calcplot3d.htm

might be useful :)

Answer 23

well it use to work fine, i guess they changed some stuff about

Answer 24

http://www.wolframalpha.com/input/?i=sqrt%28x%5E2%2By%5E2%29

hmmm, its conic not spherical. it comes to a point at the origin and makes bigger circles as z gets bigger and bigger

Answer 25

our topic to this is about contour plotting..

Answer 26

im not up to date on what contour plotting is, this is mostly from an old, decripid memory :)

Answer 27

for your private message

z = k

z = x^2 + y

for what values of x^2 + y does k = the stated set of values

Answer 28

x^2 + y = -2

when y=-x^2 -2