Question
A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is
-
-1/4
-
-4
-
-2
-
-1/2
Solution
C.
-2
The slope of line PQ 
Let 'm' be the slope of the line PQ, then the equation of PQ is
y -2 = m (x-1)
Now, PQ meets X-axis at P 
and y-axis at Q (0,2-m)
⇒ 
Now, f'(m) = 0
m = ± 2
f(2) =0
f(-2) = 8
Since, the area cannot be zero, hence the required value of m is -2
