Answer:
x² + y² + 4x - 2y + 1 = 0
Explanation:
To find the equation of a circle center at (-2,1) and passing through (-4,1), First we need to find its radius
To find its radius, we use (-2, 1) and (-4, 1)
r² =
r² = ( -4 - -2)² + ( 1-1)²
r² = (-4 +2)² + 0
r² = (-2)²
r² = 4
Equation of a circle is
(x - a)² + (y-b)² = r²
where (a, b) are the center of the circles
From the question;
The circle passes through the center (-2, 1), so our a = -2 and b = 1
We can now substitute our variables into the equation;
(x - a)² + (y-b)² = r²
(x - -2)² + (y -1)² = 4
(x+2)² + (y-1)² =4
we can now go ahead and expand the brackets
x² + 4x + 4 + y² - 2y + 1 = 4
We can rearrange this equation and hence;
x² + y² + 4x -2y +4 + 1 = 4
x² + y² + 4x -2y + 5 = 4
x² + y² + 4x -2y + 5-4 = 0
x² + y² + 4x -2y + 1 = 0