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rainbow22
 2 years ago
Center of a circle with this equation:
y^26x8y+20=x^2
rainbow22
 2 years ago
Center of a circle with this equation: y^26x8y+20=x^2

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Mertsj
 2 years ago
Best ResponseYou've already chosen the best response.0Get the variables on the left and the constant term on the right. complete the square twice and write the equation in the form: \[(xh)^2+(yk)^2=r^2\]

rainbow22
 2 years ago
Best ResponseYou've already chosen the best response.0I did but I end up with what I believe is the wrong answer. Okay, so obviously it would be (x4)^2+(y3)^3=20

rainbow22
 2 years ago
Best ResponseYou've already chosen the best response.0I am confused as to what to do with the neg.

rainbow22
 2 years ago
Best ResponseYou've already chosen the best response.0The neg in front of the twenty

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.2y^26x8y+20=x^2 x^2 +y^26x8y+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
 2 years ago
Best ResponseYou've already chosen the best response.0Nothing. It will be gone because you will be adding numbers to the right and the left sides.

Mertsj
 2 years ago
Best ResponseYou've already chosen the best response.0Ok. callisto wants to help you now. Good bye and good luck.

rainbow22
 2 years ago
Best ResponseYou've already chosen the best response.0center is therefore.. (3,4) right?

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.2No... the sign is not correct

rainbow22
 2 years ago
Best ResponseYou've already chosen the best response.0So basically it's still the same center as it would be without the negatives...?

rainbow22
 2 years ago
Best ResponseYou've already chosen the best response.0Okay. Also, what the radius would be sqrtroot of 20.. right?

rainbow22
 2 years ago
Best ResponseYou've already chosen the best response.0Sorry, but just for conformation.. It doesn't matter if there is a negative for the 'r', the center would still be the same.

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.2Nope.. \[r = \sqrt { (D/2)^2 + (E/2)^2 F}\]

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.2D=6, E=8 , F=20 in your case. Put the numbers into it and solve, what would you get for r?

rainbow22
 2 years ago
Best ResponseYou've already chosen the best response.0That.. doesn't make sense though. The radius is typically sqroot of \[(xh)^2 + (yk)^2=r^2\]

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.2So, let's do the completing square once y^26x8y+20=x^2 x^2 + y^26x8y+20= 0 x^2 6x +y^28y+20 =0 (x^2 6x +9 9) +(y^28y +16 16)+20 =0 (x^2 6x +9) +(y^28y +16) 9 16 +20 =0 (x3)^2 + (y4)^2  5 =0 (x3)^2 + (y4)^2 = 5 (x3)^2 + (y4)^2 =[ sqrt (5) ]^2 r = sqrt 5 It DOES make sense
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