Question

Complete the square and write the equation in standard form. Then give the center and radius of the circle. 10x2 + 10y2 = 100

2 + y2 = 10 (0, 0), r = 10


x2 + y2 = 100 (0, 0), r = 10

x2 + y2 = 10 (0, 0),

r = 10‾‾‾√

(x - 10)2 +(y - 10)2 = 10 (10, 10),

r = 10‾‾‾√

Answer 1

Equation: x² + y² = 10

center = (0, 0)

radius = √10

Explanation:

The general equation of a circle is ;

(x - a)² + (y - b)² = r²

Where (a, b) is the coordinate of the center of the circle, and r is its radius.

Where the center is (0,0), the equation becomes,

x² + y² = r²

In our case we have;

10x² + 10y² = 100

dividing both side by ten,

x² + y² = 10

∴ center = (0, 0)

radius = √10

Answer 2

Center: (0,0)

Radius:
`r=√(10)`

Explanation:

The given circle has equation

`10x^2+10y^2=100`

In order to complete the square, we must make sure the coefficient of the quadratic terms are unity.

We divide through by 10 to obtain;

`x^2+y^2=10`

The coefficient of the linear terms of both variables are zero.

Therefore the equation can be rewritten as;

`(x-0)^2+(y-0)^2=10`

Comparing to
`(x-h)^2+(y-k)^2=r^2`

We have (h,k)=(0,0) to the center of the circle and
`r=√(10)` to be the radius of the circle.