Because the x coordinate of (2a,a) is 2 times the y-coordinate,
the set of points (2a,a) is the set of points in which 
each x coordinate is 2 times the y coordinate, which is

  x = 2y

So we draw the graphs of x²-2x-4y+3 = 0 and x = 2y



Since (2a,a) is INSIDE the parabola, we need to find the
part of the line that is inside the parabola, so we need
to find the points where the line intersects the parabola,
by solving this system:



Solve this by substituting 2y for x in the first equation,
and solving the resulting quadratic and we find the two
points to be 

 and 



All the points on the line are of the form (2a,a), but
We only want the points of the form (2a,a) that are inside the 
parabola. So we only want the part of the line which is between
the two circles, this green part:



and the values of "a" and the values of "x" on the x-axis
that are between 1 and 3:



answer: the interval {a|1 < a < 3} or (1,3) in interval notation.

Edwin