A straight line `L` is perpendicular to the line `5x-y=1` . The area of the triangle formed by line `L ,` and the coordinate axes is 5. Find the equation of line `Ldot`

Answer

`x+5y+-5sqrt(2) = 0`

Explanation

The given line is 5x-y=1. Therefore, the equation of line L which is perpendicular to the given line is x+5y`=lambda`. This line meets the coordinates axes at `A(lambda, 0) " and B" (0,lambda//5)`.

`therefore " Area of "Delta OAB = (1)/(2) xx OA xx OB`
`"or " 5 = (1)/(2) xx lambda xx (lambda)/(5)`
`"or " lambda^(2) = 5^(2) xx 2`
`"or " lambda = +-5sqrt(2)`
Hence, the equation of line L is
`x+5y-5sqrt(2) = 0 or x +5y+5sqrt(2) = 0`