Equations of locus

1. A is the point (4,0). A variable point B moves on the curve
4x^2 + 25y^2 = 100.
Find the equation of the locus of the mid-point of AB.

2. Given L:x = -4 and C:y^2 = 8x.
A line parallel to the x-axis cuts C at P and L at Q.
Find the equation of the locus of the mid-point od PQ.

3. A(1,0) is a fixed point.
B is a variable point on the parabola y^2 = 4x.
P is the mid-point od AB.
Find the equation of the locus of P.