# What will be the equation of the locus which is at the same distance from (3,7) and (-2,4).

2
by Ark01

2014-08-19T23:32:33+05:30
Let say the point P(x, y) is on the locus. Now (x, y) is at the same distance from (3, 7) and (-2, 4).

Formula :- Distance between two points (a, b) and (c, d) =

Distance between (x, y) and (3, 7) =

Distance between (x, y) and (-2, 4) =

Now,

5x + 3y = 19

2014-08-20T00:00:24+05:30

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Find middle point P of the two  given points : [ (3-2)/2 , (7+4)/2  ]
= ( 0.5 , 5.5 )
The locus passes through this.  The locus is a straight line bisecting perpendicularly the line joining the given points.  So find slope of the line joining given points.
slope =  (7- 4) / (3 +2 )  = 3/5 = 0.6
Now the perpendicular bisector has as slope of  - 1/0.6
So equation of the locus desired :
(y - y1)    =  m (x - x1)
y - 5.5 = - (x -0.5) / 0.6
0.6 y - 5.5*6 = - x  + 0.5

0.6 y + x = 3.8      or  3 y + 5 x = 19