Your friend has no machine but has a ruler a compass a Tsqua

Your friend has no machine, but has a ruler, a compass, a T-square, and a triangle. Tell your friend how to plot a lot of points on the ellipse
      (x/4)^2 + (y/2)^2 = 1
by drawing concentric circles and then moving horizontally or vertically from well-chosen points on the circles.

Solution

Choose a point(centre of ellipse) on the paper or the sheet and draw two concentric circles equal to 2 and 1 units(major and minor diameters).Draw the major and minor diameters. Construct a line at the center at any angle and mark two points(say A and B) where the line meets smaller circle. The line also meets the bigger circle at two points say C and D. From points A and B, draw lines parallel to the major diameter. From C and D draw lines parallel to major diameter. The intersection of the lines from A and D is point F, and from B and C is point G. Points F & G lies on the ellipse. Extend lines FD & BG and lines AF and GC to obtain two more points in the other quadrants. Repeat these steps to create more points in each quadrant and then draw a smooth curve through the points.