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**1. Homework Statement**

A line passing through the point (1,0) cuts the curve Y^2=4x at two points A and B. Find the equation of the locus of the mid-point of AB.

**2. Homework Equations**

**3. The Attempt at a Solution**

the graph is parabola, the solution should also be a parabola with x-intercept at (1,0).

tried to set up 2 equations are mixed together but didn't work out

wondering if parametric equation should be used

i think i should try to find a general expression for x and y, then use mid point respectively, then mix the parametric equation

please help