Question

How do you graph `x² + y² - 2x - 8y + 16 =0`?

Answer 1

circle: centre (1 , 4 ) , r = 1

Explanation:

The general equation of a circle is

`x^2 + y^2 + 2gx + 2fy + c = 0`

`x^2 + y^2 - 2x - 8y + 16 = 0 " is in this form "`

and by comparison of the 2 equations

2g = -2 → g = -1 , 2f = - 8 → f = - 4 and c = 16

centre = ( - g , -f ) = ( 1 , 4 )

and `r = sqrt(g^2 + f^2 - c ) = sqrt((-1)^2 +(-4)^2 - 16) = 1`