Question

The equation of a circle is x2 plus y2-6x plus 2y equals 6 what are the coordinates of the center and the length of the radius of the circle

Answer 1

Explanation:

hello :

x2 plus y2-6x plus 2y equals 6 means :

x²+y²-6x+2y =6

(x²-6x)+(y²+2y)=6

(x²-6x+9 -9 )+(y²+2y+1-1) = 6

(x-3)²-9 +(y+1)²-1 = 6

(x-3)²+(y+1)² = 4²

standard form when the center is : (3;-1) and length of the radius is :4

Answer 2

(3, -1); 4

Explanation:

x² + y² - 6x + 2y = 6

Strategy:

Convert the equation to the centre-radius form:

(x - h)² + (y - k)² = r²

The centre of the circle is at (h, k) and the radius is r

Solution:

Keep the x- and y-terms together.

x² - 6x + y² + 2y = 6

1. Complete the square for x

(Take half the coefficient of x, square it, and add to each side of the equation)

(x² - 6x + 9) + y² + 2y = 15

2. Complete the square for y

(x² - 6x + 9) + (y² + 2y + 1) = 16

3. Express the result as the sum of squares

(x - 3)² + (y + 1)² =4²

h = 3; k = -1; r = 4

The centre of the circle is at (3, -1) and the length of the radius is 4.

The graph of the circle below has its centre at (3, -1) and radius 4.