A variable line cuts n given concurrent straight lines at `A_1,A_2...A_n` such that `sum_(i=1)^n 1/(OA_i)` is a constant. Show that it always passes through a fixed point, O being the point of intersection of the lines

Sum of the reciprocal intercepts on the axes by a moving straight line in its all position remain constant .Show that straight line always passes throguh a fixed point .

Show that the straight line (a+2b)x+(a-3b)y+b-a=0 always passes through a fixed point , find the cootdinates of that fixed point.

Show that the straight line (a + 2b) x + (a -3b)y + b -a = 0 always passes through a fixed point. Find the co-ordinate of that point.

A straight line moves in such a manner that the sum of the reciprocals of its intercepts upon the axes is always constant. Show that the line passes throught a fixed point .

If 3a +2b+c=0 for all positions of the moving line ax+by+c=0 , show that the line always passes through a fixed point . Find the coordinates of that fixed point.

Let L_1=0a n dL_2=0 be two fixed lines. A variable line is drawn through the origin to cut the two lines at R and SdotPdot is a point on the line A B such that ((m+n))/(O P)=m/(O R)+n/(O S)dot Show that the locus of P is a straight line passing through the point of intersection of the given lines R , S , R are on the same side of O)dot

A variable straight line AB intersecting the x and y-axies at A and B always passes through a fixed point (alpha,beta) . Find the locus of the point dividing AB in the ratio 2:1 .

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.

If a , b , c are in A . P ., then the straight line ax + 2 by + c = 0 will always pass through a fixed point whose coordinates are _

Let a x+b y+c=0 be a variable straight line, whre a , ba n dc are the 1st, 3rd, and 7th terms of an increasing AP, respectively. Then prove that the variable straight line always passes through a fixed point. Find that point.