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

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.

If a ,b ,c are variables such that 3a+2b+4c=0 , then show that the family of lines givenby a x+b y+c=0 pass through a fixed point. Also, find that 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.

Let a ,\ b ,\ c be parameters. Then the equation a x+b y+c=0 will represent a family of straight lines passikng through a fixed point iff there exists a linear relation between a , b ,\ a n d\ c dot

Prove that the line x(a+2b) + y (a-3b)=a-b passes through a fixed point for different values of a and b . Also find the fixed point.

Show that the straight lines given by (2+k)x+(1+k)y=5+7k for different values of k pass through a fixed point. Also, find that point.

Show that the lines represented by x(a+3b)+y(2a-b)=5a+b pass through a fixed point for different values of a and b .

Find the equation of a line which passes through the point (1,3) and makes equal intercepts on X and Y -axis.