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Sagot :
Answer:
Center: (-2, 4)
Radius: 4
Step-by-step explanation:
To find the centre and radius, we require to identify g , f and c
By comparing the coefficients of 'like terms' in the given equation with the general form.
2g = 4 → g = 2 , 2f = -8 → f = -4 and c = 4 → center=(−g,−f)=(−2,4)
radius = √22+(−4)2−4= √4+16−4=4
Center: (-2, 4)
Radius: 4
Hope This Helps! :)
Answer:
The center is located at (2, -4) and the radius is 4
Step-by-step explanation:
short explantion: I took the test and it was right
actual explantion: to find the center and the radius of a circle when given an equation, you are going to complete the square
- our first step is to put it into an easier format to work with
- so our new equation looks like this now
- (x²-4x)+ (y²-8y)= -4
- next we are going to complete the square:
- to do so, we are going to take our coeficents, and divide them by 2 then square them and add them to both sides of the equation
- heres the process shown out:
- (x²-4x)+ (y²+8y)= -4
- half of -4 is 2 then squared is 4
- half of 8 is 4 then squared is 16
- adding it to both sides of the equation it look like this now:
- (x²-4x+4) + (y²+8y+16)= -4 +4 +16
- next, we are going to clean up the equation and finish the square:
- on the left side with the x's:
- (x²- 4x+4) becomes (x-2)²
- the other part with the y's:
- (y²+ 8y+ 16) becomes (y+4)²
- the right side:
- -4 + 4+16 = 16
- the finalized equation looks like this:
- (x-2)² + (y+4)²= 16
- now we can take the center and the radius out of the equation in this form, (x-h)² + (y-k)² =r² when the center is (h,k)
- so the center is actaully going to be the opposite of what is in the parenthesis, since we have to take it out of the equation:
- (x-2)² = h= 2
- (y+4)² = k= -4
- our radius is going to be under the square root, because its not being squared when we re-wrote the equation:
- 16 taken the square root= √16 = 4
- so our center is (2, -4) and the radius is 4
- thank you so much for reading my answer and I really hope this helped! comment below is you need addtional clarifacation!
~addison~
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