Unofficialllyy
  • Unofficialllyy
Will fan and medal!!
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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Unofficialllyy
  • Unofficialllyy
Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credit. x2 + 2x + y2 + 4y = 20
Unofficialllyy
  • Unofficialllyy
\[x^2+2x+y^2+4y=20\]
Unofficialllyy
  • Unofficialllyy
@welshfella

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Unofficialllyy
  • Unofficialllyy
I know I have to complete the square but I have no clue how to do it.
welshfella
  • welshfella
convert it to the form (x - a)^2 + (y - b)^2 = r^2 complete the square x^2 + 2x and y^2 + 4y
Unofficialllyy
  • Unofficialllyy
We use (h-k)^2+(y-k)^2=r^2 but it's the same thing as the form you gave me.
welshfella
  • welshfella
x^2 + 2x + y^2 + 4y = 20 (x + 1)^2 - 1 + (y + 2)^2 - 4 = 20 to complete the square you take half of the coefficient of x then you have to subtract this value squared (x + 1)^2 = x^2 + 2x + 1 - so you have to subtract 1^2 from this to make x^2 + 2x
welshfella
  • welshfella
(x + 1)^2 + (y + 2)^2 = 20+1 + 4 = 25 so if you compare this with the general equation you'll see that center = (-1,-2) and radius = sqrt25 = 5
Unofficialllyy
  • Unofficialllyy
Thank you so much. I have one more question if you dont mind?
welshfella
  • welshfella
well i must go in 10 minutes so we'll see how much i can do in that time
Unofficialllyy
  • Unofficialllyy
Prove that the two circles shown below are similar.
1 Attachment
Unofficialllyy
  • Unofficialllyy
I know that all circles are similar, but how do I prove it?
welshfella
  • welshfella
oh must go now I'm sure jhannybean can help
Unofficialllyy
  • Unofficialllyy
Okay thank you!
Jhannybean
  • Jhannybean
\[x^2 + 2x + y^2 + 4y = 20\]\[(x^2+2x) + (y^2+4y)=20\]\[(x^2+2x+\color{red}{1}) +(y^2+4y+\color{red}{4})=20+\color{red}{1}+\color{red}{4}\]\[(x+1)^2+(y+2)^2=25~~~\checkmark \]
Jhannybean
  • Jhannybean
Haha you dont have to @welshfella
Unofficialllyy
  • Unofficialllyy
@Jhannybean Could you help with the circle question? It's my last one. :/
Jhannybean
  • Jhannybean
hint: try creating triangles within the circles and then using their ratios in comparison.
Jhannybean
  • Jhannybean
|dw:1440188772500:dw|
Unofficialllyy
  • Unofficialllyy
So once i have the ratios what do i do?
Jhannybean
  • Jhannybean
If we compare al the sides in a ratio, we would see it has a proportional relationship
Jhannybean
  • Jhannybean
First find the hypotenuse of both triangles, the smaller triangle having a hypotenuse of x. and the bigger one having hypotenuse of y. \[c_1 : x^2= 2^2+2^2 = 8 \iff x=\sqrt{8}\]\[c_2 : y^2=5^2+5^2 = 50 \iff y=\sqrt{50}\]
Unofficialllyy
  • Unofficialllyy
What about dilations? Couldn't we see if they are similar that way?
Jhannybean
  • Jhannybean
Then we can say by the SSS theorem, \[\frac{2}{5} = \frac{\sqrt{8}}{\sqrt{50}}\]
Jhannybean
  • Jhannybean
Hmm..i'm not really familiar with dilations! sorry.
Unofficialllyy
  • Unofficialllyy
Okay well thank you!
Jhannybean
  • Jhannybean
@cwrw238 could you help me understand dilations? :)
Unofficialllyy
  • Unofficialllyy
I understand the way you did it, and it makes perfect sense, so no worries. :) thank you for your help!
Jhannybean
  • Jhannybean
Oh cool! no problem.

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