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

• The perpendicular distance between of a line from a point $(x_1, y_1)$ is $d = \bigg| \large\frac{Ax_1+By_1+c}{\sqrt{A^2+B^2}} \bigg|$
$\qquad x+y-5=0$--------(1)
$\qquad 3x-2y+7=0$------(2)