In xy plane, a certain line L1 has how many intersections

In xy plane, a certain line L1 has how many intersections with y = x^2 +2?

1. Line L1 does not intersect the X- Axis
2. The point Q (2,1) lies on line L1

STAT1
tells us that the line is parallel to x axis. So the equation of the line will be y = k (where k is a constant)
For every value of:
k >2 we have two point of intersections. (x^2= k -2 will give two values of x)
For k =2 we have one point of intersection only point of intersection is (0,2)
and for k < 2 we Dont have any point of intersection (x^2= -ve, which is not possible)

So, 1 is insufficient

STAT2:
Statement2 by itself is nOt sufficient as we do not know the equation of the line. the line can intersect the given curve at 0 ,1 or two points.

STAT1 and STAT2 combined we have:
y=1 as the equation of the line. So we have 0 points of intersection.

So, answer will be C
Hope it helps!