Prove that the equation represent a family of lines which pass through a fixed point. Also find the fixed point : (i) `(gamma-1) x+gammay=1-3gamma`

Prove that the equation represent a family of lines which pass through a fixed point. Also find the fixed point : (ii) gammax+y=4

Show that for any value of m the equation mx- y=4m-3represents a straight line passing through a fixed point.What is the fixed point?

Prove that the family of lines represented by x(1+gamma)+y(2-gamma)+5=0 gamma being arbitrary, passes through a fixed point. Also find the fixed point.

Prove that the equation x^(2)+y^(2)-2x-2ay-8=0, a in R represents the family of circles passing through two fixed points on x-axis.

Prove that the family of lines represented by x(1+lambda)+y(2-lambda)+5=0,lambda being arbitrary, pass through a fixed point. Also find the fixed point.

Show that the equation (3-2k) x-(2+k)y=5-k, where k is real represents a family of lines all passing through a fixed point. Find the co-ordinates of this fixed point.

Statement-1: All chords of the curve 3x^(2)-y^(2)-2x+4y=0 which subtend a right angle at the origin pass through a fixed point. Statement-2: The equation ax+by+c=0 represents a family of straight lines passing through a fixed point iff there is a linear relation between a, b and c.