anonymous
  • anonymous
Thanks for helping! This question is really weird :( r=-6sin theta I need to multiply both sides of the equation by r and use r^2=x^2+y^2 to rewrite the equation in terms of x and y.
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
@Ashleyisakitty @jim_thompson5910 @zepdrix @Nnesha @e.mccormick @wio @sammixboo @kropot72 @mathmate
Astrophysics
  • Astrophysics
Ok so you want to convert it to rectangular, it's good you notice we have to multiply r and use \[r^2 = x^2+y^2\] we know the ratio for sin theta is the following \[\sin \theta = \frac{ y }{ r }\] so we have \[r = - 6\left( \frac{ y }{ r } \right)\] can you finish it off?
anonymous
  • anonymous
I'm not sure I understand where to go from there

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Astrophysics
  • Astrophysics
\[r^2 = - 6y\]
Astrophysics
  • Astrophysics
What's next?
anonymous
  • anonymous
square - 6y?
Astrophysics
  • Astrophysics
Why? Look at what we know, and we want to "get rid" of the polar coordinates.
anonymous
  • anonymous
x^2?
Astrophysics
  • Astrophysics
I don't know what that means
anonymous
  • anonymous
add it in?
Astrophysics
  • Astrophysics
Hint: \[r^2 = x^2+y^2\]
anonymous
  • anonymous
-6y=x^2+y^2?
Astrophysics
  • Astrophysics
Yes, that looks good :)
Astrophysics
  • Astrophysics
You can rearrange it and what not if you wish
anonymous
  • anonymous
That is it in terms of x and y?
anonymous
  • anonymous
I'm asked to complete the square to produce another equation in my worksheet. Should I do it from this form?
Astrophysics
  • Astrophysics
You may complete the square
Astrophysics
  • Astrophysics
Ah, yes we have to complete the square, you know how to do that right?
Astrophysics
  • Astrophysics
When you have it as such \[-6y=x^2+y^2 \] it's always best to complete the square as it will be in terms of x and y.
anonymous
  • anonymous
I know how to do it in regular form, but I'm sort of confused about this one
Astrophysics
  • Astrophysics
\[-6y = x^2+y^2 \implies x^2+y^2 + 6y = 0\]
anonymous
  • anonymous
Oh, I thought it was when you added (b/2)^2 to both sides or something like that
Astrophysics
  • Astrophysics
I didn't complete the square...I put in a form so you can complete the square.
anonymous
  • anonymous
Oh, okay gotcha
Astrophysics
  • Astrophysics
So we don't need to worry about the x^2, now complete the square for y^2+6y
Astrophysics
  • Astrophysics
When you have \[x^2+ax \implies x^2+ 2 \frac{ ax }{ 2 } + \left( \frac{ a }{ 2 } \right)^2-\left( \frac{ a }{ 2 } \right)^2\] to complete the square.
anonymous
  • anonymous
Wouldn't that make it remain the same?
anonymous
  • anonymous
Sorry, I suck at pre calc :(
Astrophysics
  • Astrophysics
You should try it, otherwise me doing everything is not going to help you :P
anonymous
  • anonymous
very true
anonymous
  • anonymous
But when plugging in y^2+6y in, it cancels back to y^2+6y, no?
Astrophysics
  • Astrophysics
Mhm, no you don't do that, we don't plug in anything I just put if you have the form y^2+6y you do the following -> .....etc
Astrophysics
  • Astrophysics
\[x^2+ax \implies x^2+ 2 \frac{ ax }{ 2 } + \left( \frac{ a }{ 2 } \right)^2-\left( \frac{ a }{ 2 } \right)^2\] \[x^2+ ax \implies y^2+6y\] in your question
anonymous
  • anonymous
y ^2+6x+9-9?
anonymous
  • anonymous
wait, no
Astrophysics
  • Astrophysics
|dw:1434416994934:dw| now we just factor
Astrophysics
  • Astrophysics
|dw:1434417167196:dw|
Astrophysics
  • Astrophysics
So now we have \[x^2+y^2+6y+9 = -9\] one step away from completing it
Astrophysics
  • Astrophysics
You were right, but you put 6x instead of 6y :P
anonymous
  • anonymous
Now I factor?
Astrophysics
  • Astrophysics
That should be = 9 not -9, yes you want it to look as such \[\huge x^2+(y+3)^2 = 9 \] that's your final answer
anonymous
  • anonymous
x^2+(y+3)^2-9=0
Astrophysics
  • Astrophysics
Good!
anonymous
  • anonymous
oh whoop, same thing ha ha
anonymous
  • anonymous
Thanks for the help!
anonymous
  • anonymous
That really helped
Astrophysics
  • Astrophysics
No problem, it makes sense now? :)
anonymous
  • anonymous
Yea a lot more!
Astrophysics
  • Astrophysics
Awesome, glad to hear it, make sure you go over it again!
anonymous
  • anonymous
Of course :), have a good day
Astrophysics
  • Astrophysics
You to, bye :)

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