Question

Question #bb165

Answer 1

The equation of line will be `4x-5y-21=0`

Explanation:

let the equation of the line be `color(red)(ax+by+c=0)->(1)`
it is given that `(1)` is perpendicular to the line `5x-4y+1=0->(2)`
line `(2)` is of the form `ax+by+c=0`
a line perpendicular to `ax+by+c=0` will be of the form`:`
`bx-ay+k=0`
hence the equation of one will be `-4x-(-5)y+k=0`
`i.e. 4x-5y-k=0->(3)`
since `(3)` passes through `(1,5)`
`rArr4(1)-5(5)-k=0rArrk=-21`
hence the equation of line will be `4x-5y-21=0`