Let's break down the problem and solve it step-by-step: **Problem Statement:** A point moves so that its distance from the point (2,0) is two-thirds its distance from the line \( y = 5 \). Derive the equation (in standard form) of the curve traced by the point, and identify the curve. --- ### 1. Let the moving point be \( (x, y) \). #### Distance from the point \((2, 0)\): \[ \text{Distance to } (2,0) = \sqrt{(x-2)^2 + (y-0)^2} = \sqrt{(x-2)^2 + y^2} \] #### Distance from the line \(y = 5\): The distance from \((x, y)\) to the line \(y = 5\) is the perpendicular distance: \[ \text{Distance to } y=5 = |y - 5| \] --- ### 2. The relationship is: \[ \text{Distance to } ( standard form of this