Two fixed points \( P \) and \( Q \) are 4 units apart and are on same side of a variable line \...

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Two fixed points \( P \) and \( Q \) are 4 units apart and are on same side of a variable line \( L \). Let \( P M \) and \( Q N \) are perpendicular distance of \( P \) and \( Q \) from line \( L \) satisfy equation \( P M+3 Q N \) \( =4 \), then line \( L \) always touches a circle \( C \)
(a) the centre of circle \( C \) lies on line \( P Q \)
(b) the radius of circle is 1
(c) the radius of circle is 2
(d) the centre of the circle \( C \) lies on perpendicular bisector of \( P Q \)
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