Question

e dist Since the radius is an imaginary value, the equation is not a real circle. the cece - 4x + 2) + ( + 8y + (-2) + + 4) = -5 2-5 r-rs-115 lisch Pe squares for each quadratic, list the center and radius, then graph each circle ahs 12.3 llowing: it tort 'onics Ibolas It wh 121, the at of anslated center: 2 - 40 = 4 (b) x² + y2 - 4x = 0 2 27 822

Answer 1

The general equation of a circle is given by

$(x-h)^2+(y-k)^2=r^2$

where (h,k) is the center of the circle and r is the radius

x² + y² -2x - 8y = 8

x² - 2x + y² - 8y = 8

(x² - 2x + ) + (y² -8y + ) = 8

Add square of half of the coefficient of x in the first paenthesis and the half of the square of the coefficient of y in the second parenthesis

Then add the two squaes at the right-hand side of the equation

(x² -2x +1 ) + (y² -8y + 16 ) = 8 + 1+ 16

(x-1)² + (y-4)² = 25

comparing this with the general equation

Center is ( 1, 4)

Radius is 5