Final answer:
To find the point on the curve that is closest to the given point, we use the distance formula. By substituting the curve equation into the formula, we can find the closest point. In this case, the closest point is (6,√3).
Step-by-step explanation:
To find the point on the curve (y²x=18) that is closest to the point (2,0), we can use the distance formula. The distance between two points, (x₁, y₁) and (x₂, y₂), is given by the formula:
distance = √((x₂ - x₁)² + (y₂ - y₁)²)
In this case, the point (2,0) is our initial point (x₁, y₁) and we need to find the other point on the curve (x₂, y₂) that minimizes the distance. By substituting y²x=18 into the distance formula, we can minimize the distance and find the closest point on the curve, which is option B: (6,√3).