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Q.

A line is drawn perpendicular to line y = 5x, meeting the coordinate axes at A and B. If the area of triangle OAB is 10 sq. units, where O is the origin, then the equation of drawn line is 

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a

x+4y=10

b

x−4y=10

c

x−5y=10

d

x+5y=10

answer is A.

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Detailed Solution

 Let the equation of line be 

Question Image

xa+yb=1

AB is perpendicular to y=5x. Hence, −ba×5=−1 or 5b=a

 Area of ΔOAB=12|ab|

 or 10=125b2 or b2=4 or b=±2,a=±10

The line can be 

x10+y2=1 or x10+y2=−1

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