# How do you find the center and radius of the circle # x^2-2x+y^2-8y+1=0#?

##### 2 Answers

Radius:

Centre:

#### Explanation:

You should convert to the form

Our goal here is to make the expressions in parentheses into perfect squares. We can use the formula

So,

We need to add **and** subtract this number inside the parentheses to keep the equation equivalent.

The radius of a circle in the form

Hopefully this helps!

You complete the squares by adding

#### Explanation:

The standard Cartesian form for the equation of a circle is:

where

Equation [2] is the same as equation [1] but with the squares expanded and equation [3] is the given equation with some spaces added for missing terms:

Let's try to make equations [2] and [3] match by adding

Subtract 1 from both sides of equation [4] and label it equation [5]:

Now that equation [2] and equation [5] both have 6 terms on the left side, we can see that we can find the value of h by equating the second term in equation [2] with the same term in equation [5]:

Substitute 1 for h into equation [5] and number it equation [6]:

We can find the value of k by equating the fifth term in equation [2] with the same term in equation [5]:

Substitute 4 for k into equation [6] and number it equation [7]:

Because we used the patterns for

Simplify the right side:

Comparing equation [9] with equation [1], we can see that the center is