Using the following equation, find the center and radius: x2 −2x + y2 − 6y = 26 (5 points)

Center: (1,3)

Radius: 6

Step-by-step explanation:

Hi there!

Typically, the equation of a circle would be in the form where is the center and is the radius.

To get the given equation into this form, we must complete the square for both x and y.

1) Complete the square for x

Let's take a look at this part of the equation:

To complete the square, we must add to the expression the square of half of 2. That would be 1² = 1:

Great! Now, let's add this to our original equation:

We cannot randomly add a 1 to just one side, so we must do the same to the right side of the equation:

Complete the square:

2) Complete the square for y

Let's take a look at this part of the equation :

To complete the square, we must add to the expression the square of half of 6. That would be 3² = 9:

Great! Now, back to our original equation:

Remember to add 9 on the other side as well:

Complete the square:

3) Determine the center and the radius

Now, we can see that (1,3) is in the place of (h,k). 36 is also in the place of r², making 6 the radius.

I hope this helps!

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step-by-step explanation:

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