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Find the center and the radius of the circle with the equation:

x2 + 2x + y2 – 2y - 14 = 0

a. center: (1,-1)

C. center: (2,-2)

radius: 4

radius: 14

b. center: (-1,1)

d. center: (-2,2)

radius: 4

radius: 14

Please select the best answer from the choices provided

User Groomsy
by
8.1k points

2 Answers

6 votes

Answer:

B. Center: (-1,1)

radius: 4

Explanation:

User Mihey Mik
by
8.4k points
7 votes

Answer:


(x+1)^2 + (y-1)^2 = 16

And the general formula for a circle is given by this expression:


(x-h)^2 +(y-k)^2 = r^2

With the center (h,k) and the radius r. If we compare this general expression with the formula that we obtain in (1) we see that :


h = -1, k =1 , r =4

So then the best solution for this cae would be:

b. center: (-1,1)

radius =4

Explanation:

For this case we have the following equation given:


x^2 +2x + y^2 -2y -14=0

And we can complete the squares for this case like this:


x^2 +2x +(2/2)^2 +y^2 -2y +(2/2)^2 =14 +1+1


(x^2 +2x +1) +(y^2 -2y +1) =16

Now we can rewrite the last expression like this:


(x+1)^2 + (y-1)^2 = 16

And the general formula for a circle is given by this expression:


(x-h)^2 +(y-k)^2 = r^2

With the center (h,k) and the radius r. If we compare this general expression with the formula that we obtain in (1) we see that :


h = -1, k =1 , r =4

So then the best solution for this cae would be:

b. center: (-1,1)

radius =4

User Lewis McGeary
by
8.1k points

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