Answer:
radius = 7 units
Step-by-step explanation:
We are given the equation;
x² - 10x + y² - 10y = -1
We are required to determine the radius of the circle;
We are going to use completing square method to solve for the radius and the center of the circle.
First we make sure the coefficient of x² and y² is 1
x² - 10x + y² - 10y = -1
Then we add the square of half the coefficient of x and y on both sides of the equation;
That is;
[tex]x^2- 10x+(\frac{-10}{2})^2 + y^2+- 10y +( \frac{-10}{2})^2= -1 +(\frac{-10}{2})^2+ (\frac{-10}{2})^2[/tex]
Simplifying the equation, we get;
[tex](x-\frac{10}{2})^2 + (y-\frac{10}{2})^2= -1+25+25[/tex]
Thus;
[tex](x-\frac{10}{2})^2 + (y-\frac{10}{2})^2= 49[/tex]
That is;
[tex](x-5)^2 + (x-5)^2 = 49[/tex]
The equation of a circle is written in the form of;
[tex](x-a)^2+(x-b)^2=r^2[/tex]
Then (a, b) is the center and r is the radius.
Therefore;
In our case; [tex](x-5)^2+(y-5)^2=49[/tex]
Then, center = ( 5, 5)
radius = √49
= 7 units
