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

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

The lines (a +2b)x +(a – 3b)y= a - b for different values of a and b pass through the fixed point whose coordinates are

The line (p+2q)x+(p-3q)y=p-q for different values of p and q passes through the point

Consider the equation y-y_1=m(x-x_1) . If ma n dx_1 are fixed and different lines are drawn for different values of y_1, then (a)the lines will pass through a fixed point (b)there will be a set of parallel lines (c)all the lines intersect the line x=x_1 (d)all the lines will be parallel to the line y=x_1

If aa n db 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 non-zero numbers a, b, c are in H.P., then the straight line (x)/(a)+(y)/(b)+(1)/(c)=0 always passes through a fixed point. That point is

Statement 1 : The equation x^2+y^2-2x-2a y-8=0 represents, for different values of a , a system of circles passing through two fixed points lying on the x-axis. Statement 2 : S=0 is a circle and L=0 is a straight line. Then S+lambdaL=0 represents the family of circles passing through the points of intersection of the circle and the straight line (where lambda is an arbitrary parameter).

If a , b ,c are in harmonic progression, then the straight line ((x/a))+(y/b)+(1/c)=0 always passes through a fixed point. Find that point.

A quadrilateral is inscribed in a parabola y^2=4a x and three of its sides pass through fixed points on the axis. Show that the fourth side also passes through a fixed point on the axis of the parabola.