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。