A line is such that its segment between the straight lines 
and 
is bisected at the point (1, 5), then its equation is
Text Solution
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Any line through the middle point M (1, 5) of the intercept AB may be taken as
…..(i)
where ‘ r ’ is the distance of any point ( x , y ) on the line (i) from the point M (1, 5).
Since the points A and B are equidistant from M and on the opposite sides of it, therefore if the coordinates of A are obtained by putting r=d in (i), then the co-ordinates of B are given by putting 
.
Now the point 
lies on the line 
and point 
lies on the line 
.
Therefore, 
and 
Eliminating ‘ d ’ from the two, we get 
.
Hence the required line is 
or 
.
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