Question

the area of circle x²+y²+2x+2y+1=0 is ?

Answer 1

we know ,
x² + y² + 2gx + 2fy + C = 0
Radius of given circle = √{g² + f²-C}
use this here,

Radius = √{(1)² + (1)² - 1} = 1 unit .

area of circle = πr²
= π (1)² = π unit²

Answer 2

The equation of given circle can be written as:

(x+1)^2 + (y+1)^2 = 1

which gives us the
centre of circle = (-1,-1)
radius = 1

Area of circle = πr^2 = π(1)^2 = π units.