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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

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

Grade:7

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 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
askIITians Faculty

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