The equation of a circle is: \[ (x - h)^2 + (y - k)^2 = r^2 \] Given points: (-1,1) and (2,1)
Center (h, k) lies on the line: \[ h + 2k + 3 = 0 \quad \Rightarrow \quad h = -2k - 3 \] Since the distances from the center to both points must be equal, solving gives: \[ h = \frac{1}{2}, \quad k = -\frac{7}{4} \] Using the distance formula, \[ r^2 = \frac{157}{16} \] Expanding \((x - h)^2 + (y - k)^2 = r^2\) results in: \[ 2x^2 + 2y^2 - 2x + 7y - 13 = 0 \]