anonymous
  • anonymous
Center of a circle with this equation: y^2-6x-8y+20=-x^2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Mertsj
  • Mertsj
Get the variables on the left and the constant term on the right. complete the square twice and write the equation in the form: \[(x-h)^2+(y-k)^2=r^2\]
anonymous
  • anonymous
I did but I end up with what I believe is the wrong answer. Okay, so obviously it would be (x-4)^2+(y-3)^3=-20
anonymous
  • anonymous
I am confused as to what to do with the neg.

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Mertsj
  • Mertsj
What negative?
anonymous
  • anonymous
The neg in front of the twenty
Callisto
  • Callisto
y^2-6x-8y+20=-x^2 x^2 +y^2-6x-8y+20= 0 centre = (-D/2 , -E/2) in the form x^2 +y^2+Dx+Ey+F= 0 Therefore centre = ( -(-6/2) , -(-8/2) ) =...... Can you do it now?
Mertsj
  • Mertsj
Nothing. It will be gone because you will be adding numbers to the right and the left sides.
Mertsj
  • Mertsj
Ok. callisto wants to help you now. Good bye and good luck.
anonymous
  • anonymous
center is therefore.. (-3,-4) right?
Callisto
  • Callisto
No... the sign is not correct
anonymous
  • anonymous
sooo it's (3,4).
anonymous
  • anonymous
So basically it's still the same center as it would be without the negatives...?
Callisto
  • Callisto
Yes
anonymous
  • anonymous
Okay. Also, what the radius would be sqrtroot of 20.. right?
anonymous
  • anonymous
Sorry, but just for conformation.. It doesn't matter if there is a negative for the 'r', the center would still be the same.
Callisto
  • Callisto
Nope.. \[r = \sqrt { (D/2)^2 + (E/2)^2 -F}\]
Callisto
  • Callisto
D=-6, E=-8 , F=20 in your case. Put the numbers into it and solve, what would you get for r?
anonymous
  • anonymous
squareroot of 5...
Callisto
  • Callisto
It should be that ...
anonymous
  • anonymous
That.. doesn't make sense though. The radius is typically sqroot of \[(x-h)^2 + (y-k)^2=r^2\]
Callisto
  • Callisto
So, let's do the completing square once y^2-6x-8y+20=-x^2 x^2 + y^2-6x-8y+20= 0 x^2 -6x +y^2-8y+20 =0 (x^2 -6x +9 -9) +(y^2-8y +16 -16)+20 =0 (x^2 -6x +9) +(y^2-8y +16) -9 -16 +20 =0 (x-3)^2 + (y-4)^2 - 5 =0 (x-3)^2 + (y-4)^2 = 5 (x-3)^2 + (y-4)^2 =[ sqrt (5) ]^2 r = sqrt 5 It DOES make sense
Callisto
  • Callisto
Here is the proof...
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