To find the equation of the sphere tangent to the plane x - 3y + 4z + 23 = 0 at the point (1, 4, -3) with a radius of √26, the normal vector to the plane is crucial as it indicates the direction toward the sphere's center. The center of the sphere can be determined by moving along the normal vector from the tangent point by the radius distance. Since the normal vector has two possible directions, there are two potential centers for the sphere. The general form of the sphere's equation can then be derived using the center coordinates and the given radius. This approach allows for the correct formulation of the sphere's equation in relation to the specified plane and point.