Question

WIll award medal
Consider the equation below.
9x2 + y2 + 9z2 – 6y – 90z + 225 = 0
reduce the equation to one of the standard forms

Answer 1

Complete the square

Answer 2

oh really?

Answer 3

how do you know right away to do that

Answer 4

Because I'm batman

Answer 5

triuu

Answer 6

Remember complete the square \[x^2+ax \implies x^2+2*\frac{ a }{ 2 }x + \frac{ a }{ 2 }^2 - \frac{ a }{ 2 }^2\]

Answer 7

yea and with three variables?

Answer 8

Yeah, do it separately for each one in one run! If that makes sense, try it out first and if you get stuck then ask for help

Answer 9

coolio

Answer 10

(y-3)^2-9(z+5)^2+9x^2=-441

Answer 11

? @iambatman

Answer 12

@ganeshie8

Answer 13

then divide by -441 to get the equation to equal 1

Answer 14

-441? Mhm I think you have messed up somewhere in your completing the square process

Answer 15

god damn... so tedious

Answer 16

9x^2 + y^2 + 9z^2 - 6y - 90z + 225 = 0

as a start group the terms wid same variables together :
(9x^2) + (y^2 - 6y) + (9z^2 - 90z) = -225

now complete the square for second and third groups

Answer 17

Yeah, I believe it should be along the lines of \[9x^2+(y-3)^2+9(z-5)^2=9\] and then you should be able to compare it with one of the quadratic surfaces and boom boom boom, it's just this stuff that can be annoying at times :P

Answer 18

awesome thank you!!!!1