If sum of the perpendicular distances of a variable point `P (x , y)`from the lines `x + 5y = 0`and `3x -2y +7 = 0`is always 10. Show that P must move on a line.

Explanation

The perpendicular distance of P(x,y) from lines (1) and (2) are respectively given by


`d_1 = |x+y-5|/sqrt(1^2+1^2)`


`d_2 = |(3x+27+7)|/ sqrt (3^2+(-2)^2)`


i.e, `d_1 = |x+y-5|/ sqrt 2`


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