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qaws [65]
3 years ago
15

1. The beginning steps for determining the center and radius of a circle using the completing the square method are shown below:

Mathematics
1 answer:
Tanzania [10]3 years ago
7 0

Answer : (x^2 - 6x + 9) + (y^2- 4y + 4) = 3 + (9 + 4)

Center is (-3,3) and radius = 4

(x + 4)^2 + (y - 3)^2 = 6^2

(1) Step 1: x^2 - 6x + y^2 - 4y = 3

Step 2: (x^2- 6x) + (y^2 - 4y) = 3

In completing the square method we take coefficient of x and divide by 2 and the square it . Then add it on both sides

The coefficient of x is -6. \frac{-6}{2} = (-3)^2 = 9

The coefficient of y is -4. \frac{-4}{2} = (-2)^2 = 4

Step : (x^2- 6x + 9) + (y^2 - 4y + 4) = 3 +9 + 4

(2) x^2 +  y^2 +  6x - 6y + 2 = 0

To find center and radius we write the equation in the form of

(x-h)^2 + (y-k)^2 = r^2 using completing the square form

Where (h,k) is the center and 'r' is the radius

x^2 +  y^2 +  6x - 6y + 2 = 0

(x^2 +  6x) +  (y^2  - 6y) + 2 = 0

In completing the square method we take coefficient of x and divide by 2 and the square it . Then add it on both sides

(x^2 +  6x + 9) +  (y^2  - 6y + 9)  = -2 + 9 + 9

(x + 3)^2 +  (x - 3)^2 = 16

Here h= -3 and k=3 and r^2 = 16 so r= 4

Center is (-3,3) and radius = 4

(c) Step 1: x^2 + 8x + y^2 -  6y = 11

Step 2: (x^2 + 8x) + (y^2 -  6y) = 11

Step 3: (x^2 + 8x + 16) + (y^2 - 6y + 9) = 11 + (16 + 9)

Step 4: (x^2 + 8x + 16) + (y^2 - 6y + 9) = 36

We factor out each quadratic

(x^2 + 8x + 16) = (x+4)(x+4) = (x+4)^2

((y^2 - 6y + 9)) = (x-3)(x-3) = (x-3)^2

Step 5 :(x + 4)^2 + (y - 3)^2 = 6^2

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