Let y 1 = √ (4-x 2)

Then its image is the upper arc of the circle X 2+Y 2 = 4.

And y2=k(x-2)+3.

Then its image is a straight line (system) passing through points (2, 3).

The problem is transformed into that when y 1 and y2 have two intersections,

Find the range of k.

① When the distance from y2 to the origin is equal to 2, k=5/ 12,

Y2 is tangent to the arc.

②y2 passes through the left end point (-2,0) of the arc,

The solution is k=3/4.

A straight line and a semi-arc between ① and ② (including ②) have two intersections.

∴5/ 12<； k≤3/4。