A line is such that its segment between the lines `5x" "" "y" "+" "4" "=" "0` and `3x" "+" "4y" "" "4" "=" "0` is bisected at the point (1, 5). Obtain its equation.

Explanation

We have, `5x−y+4=0->(1)`
`3x+4−4=0->(2)`



Let the intersection points are `(alpha_1,beta_1)`and`(alpha_2,beta_2) `respectively,

Thus, we get:

`5alpha_1−beta_1+4=0`
`beta_1=5alpha_1+4..........(3)`
`3alpha_2+4beta_2−4=0`
`beta_2=(4−3alpha_2)/4............(4) `

Now midpoint is(1,5)

So, we get

`(alpha_1+alpha_2)/2=1 and (beta_1+beta_2)/2=5`

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