A line is drawn perpendicular to line `y=5x ,` meeting the coordinate axes at `Aa n dB` . If the area of triangle `O A B` is 10 sq. units, where `O` is the origin, then the equation of drawn line is (a) `3x-y-9` (b) `x+5y=10` `x+4y=10` (d) `x-4y=10`

Options

A. 12
B. -12
C. 10
D. -10

Answer

A, B

Explanation

Let the equation of line be `(x)/(a) + (y)/(b) = 1.`

AB is perpendicular to y = 5x.
`therefore -(b)/(a) xx 5=-1 " or "5b=a`
`"Area of " Delta OAB = (1)/(2)|ab|`
`rArr 10 = (1)/(2) |5b^(2)|`
`rArr b^(2) = 4`
`rArr b = +- 2`
When b=2, a=10 " and when" b =-2, a=-10.
The line can be `(x)/(10) + (y)/(2) = 1 " or " (x)/(10) + (y)/(2) = -1.`