An equation of a circle:
(x - a)² + (y - b)² = r²
(a; b) - a coordinates of a center
r - a radius
The length of a radius is equal the distance between points (2; 8) and (-3; 4).
A distance between \(A(x_A;\ y_A)\) and \(B(x_B;\ y_B)\)
\(d=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\)
subtitute
\(d=\sqrt{(-3-2)^2+(4-8)^2}=\sqrt{(-5)^2+(-4)^2}=\sqrt{25+16}=\sqrt{41}\)
r=√41; (-3; 4) ⇒ a = -3 and b = 4
subtitute
(x - (-3))² + (y - 4)² = (√41)²
Answer: (x + 3)² + (y - 4)² = 41
