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Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credit.

x2 − 4x + y2 + 8y = −4 (10 points)

Sagot :

williamkludas

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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