Answer:
The equation of the circle is (x+4)^2 + (y+2)^2 = R^2, where R is the unknown radius. The line normal to the given line passes through the center of the circle (-4,-2). Its equation is (4x - 3y) = (-16) + (6) = -10.→ (3y - 4x) = 10, which is the equation of the diameter perpendicular to the given line. The intersection point P of the two lines is on the circumference of the circle. Solving the two equations, the intersection point P is (-1, 2).The radius R is the distance between the center(-4,-2) of the circle and P(-1,2). R^2 = (9) + (16). Radius R = 4.
