It is my undersatanding that you want to draw ellipse, hyperbola and straight line in first quadrant. Try the following code and experiment with alpha, beta and f to get the exact diagram as you need.
axis([0 20 0 1])
fun1 = @(x2,y2) y2.^2 - (x2/beta).^2 -1;
fimplicit(fun1,[0 20 0 2]);