To stretch horizontally by a factor of k, the rule is:

Replace x by x/k

So we replace x by x/2 in

        x² + y² - 2x - 3 = 0

(x/2)² + y² - 2(x/2) - 3 = 0

       x²/4 + y² - x - 3 = 0

Cl;earing of fractions:

      x² + 4y² - 4x - 12 = 0

That's all you were supposed to do.  However if you
place the circle and the ellipse in standard form
you get:

(x - 1)² + (y - 0)² = 2²

which is this graph:



And the ellipse has the standard equation

(x - 2)²   (y - 0)²
———————— + ———————— = 1
   4²         2²

and its graph is:



Edwin