Is x^2 + y^2 + 3y + 4x - 8 the equation of a circle. If yes, what is the radius.

Question

pleas

Answer 1

The circle equation is x ² + y ² + 3y + 4x - 8 = 0

Compare it to circle equation x ² + y ² + 2g x + 2f y + c = 0.

c  = -8

2g  = 4

g  = 2

2f  = 3

f  = 3/2

Center ( -g , -f ) = ( - 2 , - 3/2 )

Radius = √(g ² + f  ² - c )

= √(4 + (9/4) + 8) = √(16 + 9 + 32/4)

= √(57/4)

Radius of circle(r ) = 3.77.