Question

A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of the radius? (-7, -1), 36 units (7, 1), 36 units (7, 1), 6 units (-7, -1), 6 units NextReset

Answer 1

hello :
x² + y² + 14x + 2y + 14 = 0
(x²+14x)+(y²+2y)+14=0
(x²+2(7)(x) +7²) -7² +( y²+(2)(1)y+1²)-1² +14 = 0
(x+7)² +(y+1)² = 6²
the center : (-7,-1) and length of the radius is : 6

Answer 2

Center (-7,-1)

radius: 6

Explanation:

We need to remember that the formula of a circle with center in (h,k) and radius r is: (x-h)² + (y-k)² = r²

In this problem we have the equation x² + y² +14x +2y +14 = 0 and we need to transform it into the formula (x-h)² + (y-k)² = r²

First we're going to rearrange the terms so the terms with x are together and the terms with y are together. We are going to move the independent term (The one without a letter, 14 in this case, to the right side of the equation)

x² + y² +14x +2y +14 = 0

(x² + 14x) + (y² + 2y) = -14

Now we need to complete to perfect square trinomials. To know which term we need to add we're going to take the coefficient of the term with the x, divide it by two and then square it)

Example: for the term 14x we are going to do 14/2 = 7 and then we're going to make 7² = 49.

For the term 2y we do 2/2 = 1. 1² = 1.

So we get the next two perfect square trinomials:

(x² + 14x +49) + (y² + 2y +1)

Back to our equation, we need to add the 49 and the 1 to the other side so the equation still holds:

(x² + 14x +49) + (y² + 2y +1) = -14 +49 +1

(x² + 14x +49) + (y² + 2y +1) = 36

The parenthesis can be written as squared binomials:

(x + 7)² + (y +1)² = 36.

Now this formula is written as (x-h)² + (y-k)² = r²

Therefore, h = -7, k = -1 and r²= 36⇒ r = 6