Question

In a given plane , P is a point on line l. Consider the locus of points in the plane 3 from line l , and the locus of points in the plane h units from point P.

(a) If h=1 , the number of points of intersection of the two loco is ______ ?

(b) If h=3 , the number of points of intersection of the two loco is ______ ?

(c) If h=3.6 , the number of points of intersection of the two loco is ____ ?

Answer 1

Let's say that in the x-y plane, l is the x-axis and P is the origin.
The locus of points 3 units from l are the lines y=3 and y=-3.
The locus of points h units away from P is the circle centered at the origin with radius h.
Now, if h=1, the circle never intersects the 2 lines. = 0
For h=3, the circle intersects the lines once each. = 2
For h=3.6, the circle intersects the lines twice each. = 4