# a line is drawn through a point [1,2] to meet the coordinate axis at P and Q such that the area of triangle OPQ where o is origin is LEAST then slope of line PQ is....a.-1/2 b.-2 c.-1/4 d.-4

Jitender Singh IIT Delhi
8 years ago
Ans. -2
Equation of line with x-intercept ‘a’ and y-intercept ‘b’ is:
$\frac{x}{a} + \frac{y}{b} = 1$
OP = a, OQ = b
Area of triangle OPQ = A = ½ ab
Line is passing through [1,2],
$\frac{1}{a} + \frac{2}{b} = 1$
$b = \frac{2a}{a-1}$
$A = \frac{a^{2}}{a-1}$
To minimize the area, dA/da = 0
$\frac{dA}{da} = \frac{a^{2}-2a}{(a-1)^{2}} = 0$
a = 0, 2
At a = 0, Area = 0 Not Possible
a = 2 is minima
$b = \frac{2a}{a-1} = 4$
$Slope = \frac{-b}{a} = \frac{-4}{2} = -2$
Cheers!
Thanks & Regards
Jitender Singh
IIT Delhi