Show that the straight lines given by `x(a+2b)+y(a+3b)=a` for different values of a and b pass through a 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.

Use the graphical method to show that the straight lines given by the equations x+y=2, x-2y=5 and x/3+y=0 pass through the same 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.

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 .

If a and b are two arbitrary constants, then prove that the straight line (a-2b)x+(a+3b)y+3a+4b=0 will pass through a fixed point. Find that point.

If a + 2b + 3c = 0 " then " a/3+(2b)/3+c=0 and comparing with line ax + by + c, we get x = 1/3 & y = 2/ 3 so there will be a point (1/3,2/3) from where each of the lines of the form ax + by + c = 0 will pass for the given relation between a,b,c . We can say if there exists a linear relation between a,b,c then the family of straight lines of the form of ax + by +c pass through a fixed point . If a , b,c are in A.P., then the line ax + 2by + c = 0 passes through

If a + 2b + 3c = 0 " then " a/3+(2b)/3+c=0 and comparing with line ax + by + c, we get x = 1/3 & y = 2/ 3 so there will be a point (1/3,2/3) from where each of the lines of the form ax + by + c = 0 will pass for the given relation between a,b,c . We can say if there exists a linear relation between a,b,c then the family of straight lines of the form of ax + by +c pass through a fixed point . If a , b, c are consecutive odd integers then the line ax + by + c = 0 will pass through

Show that equation x^2+y^2-2ay-8=0 represents, for different values of 'a, asystem of circles"passing through two fixed points A, B on the X-axis, and find the equation ofthat circle of the system the tangents to which at AB meet on the line x+ 2y + 5 = 0 .

If the algebraic sum of perpendiculars from n given points on a variable straight line is zero then prove that the variable straight line passes through a fixed point

A circle passes through a fixed point A and cuts two perpendicular straight lines through A in B and C. If the straight line BC passes through a fixed-point (x_(1), y_(1)) , the locus of the centre of the circle, is