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

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

If t_1 a n d t_2 are roots of eth equation t^2+lambdat+1=0, where lambda is an arbitrary constant. Then prove that the line joining the points (a t1,22a t_1)a d n(a t2,22a t_2) always passes through a fixed point. Also, find the point.

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.

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.

Find the normal to the curve x=a(1+costheta),y=asinthetaa tthetadot Prove that it always passes through a fixed point and find that fixed point.

A family of lines is given by (1+2lambda)x+(1-lambda)y+lambda=0 being a parameter . The line belonging to this family at the maximum distance from the point (1,4) is ax+by+c=0 , then find the value of (a+b+c)/16

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.

If 3a + 2b + 6c = 0 the family of straight lines ax+by = c = 0 passes through a fixed point . Find the coordinates of fixed point .