3.5b Nature of the Roots (Combination of Straight Line and a Curve)

Example 2 (Combination of Straight Line and a Curve)
The straight line y=2k+1   intersects the curve y=x+k2x   at two distinct points.  Find the range of values of k.







Example 3 (Straight Line does not intersect the curve)
Find the range of values of m for which the straight line y=mx+6   does not meet the curve 2x2xy=3  .