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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


6 years ago

Jitender Singh
IIT Delhi
158 Points
							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, 2At a = 0, Area = 0   Not Possiblea = 2 is minima$b = \frac{2a}{a-1} = 4$$Slope = \frac{-b}{a} = \frac{-4}{2} = -2$Cheers!Thanks & RegardsJitender SinghIIT DelhiaskIITians Faculty

6 years ago
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• 53 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions