Question

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

Answer 1

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

Step-by-step 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