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Question

If the lines passing through the points (2,3),(K2,6) and (6,4),(K,6) are parallel, then the total number of possible real values of K is

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Solution

m1= Slope of line passing through (2,3),(K2,6)
=3K22
m2= Slope of line passing through (6,4),(K,6)
=2K6
As lines are parallel. So
m1=m23K22=2K6
3K18=2K24
2K23K+14=0
As D<0, so no real value of K is possible.

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