Question

15. Determine and state the coordinates of the center and the length of the radius of a

circle whose equation is x2 + y2 – 6x = 56 - 8y.
PLEASEEE HELP!!!

Answer 1

(3, - 4 ), r = 9

Explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² + y² - 6x = 56 - 8y ( add 8y to both sides )

x² + y² - 6x + 8y = 56 ( collect x and y terms together )

x² - 6x + y² + 8y = 56

Use the method of completing the square

add ( half the coefficient of the x/y term )² to both sides

x² + 2(- 3)x + 9 + y² + 2(4)y + 16 = 56 + 9 + 16

(x - 3)² + (y + 4)² = 81 ← in standard form

with centre = (3, - 4 ) and r =
`√(81)` = 9