Question

A line is such that it's segment between the lines 5x-y+4=0 and 3x+4y-4=0 is bisected at the point (1,5). obtain it's equation?

Answer 1

Step-by-step explanation:

Given lines are,

5x−y+4=0       ...... (1)

3x+4y−4=0     ...... (2)

Let AB be the segment between the lines (1) and (2) and point P (1,5) be the mid-point of AB.

Let the points be A(α1,β1).

It is given that the line segment AB is bisected at the point P (1,5). Therefore,

⇒(1,5)=(2α1+α2,2β1+β2)

So,

2α1+α2=1

α1+α2=2

α2=2−α1    ...... (3)

Also,

2β1+β2=5

β1+β2=10

β2=10−β1        ...... (4)

Point A and B lie on lines (1) and (2), respectively. Therefore, from lines (1) and (2), we have

5α1