Question

Find the radius of the circle whose equation is x² - 10x + y² - 10y = -1.

1
7
49

Answer 1

radius = 7 units

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;

`x^2- 10x+((-10)/(2))^2 + y^2+- 10y +( (-10)/(2))^2= -1 +((-10)/(2))^2+ ((-10)/(2))^2`

Simplifying the equation, we get;

`(x-(10)/(2))^2 + (y-(10)/(2))^2= -1+25+25`

Thus;

`(x-(10)/(2))^2 + (y-(10)/(2))^2= 49`

That is;

`(x-5)^2 + (x-5)^2 = 49`

The equation of a circle is written in the form of;

`(x-a)^2+(x-b)^2=r^2`

Then (a, b) is the center and r is the radius.

Therefore;

In our case;
`(x-5)^2+(y-5)^2=49`

Then, center = ( 5, 5)

radius = √49

= 7 units