Final answer:
The point on the ellipse 3x^2 + y^2 = 3 furthest from the point (1, 0) is (-√3, 0), since it is the farthest point on the major axis from (1, 0).
Step-by-step explanation:
To find the points on the ellipse 3x2 + y2 = 3 that are farthest away from the point (1, 0), you first need to write down the equation of the ellipse in its standard form by dividing each term by three: x2 + (y2/3) = 1. This represents an ellipse that is centered at the origin (0, 0) with a horizontal axis equal to the square root of 3 and a vertical axis equal to the square root of 1 (which is 1).
To find the furthest points from (1, 0), consider that the farthest points on an ellipse from any point not at the center are along the major axis, which in this case is horizontal. Therefore, the points on the ellipse farthest from (1, 0) are (-√3, 0) and (√3, 0). However, because (1, 0) is closer to (√3, 0), the point farthest away from (1, 0) is (-√3, 0).