Two fixed points A and B are taken on the coordinates axes such that OA=a and OB =b. Two variable points A' and B' are taken on the same axes such that OA'+OB' = OA+OB. Find the locus of the point of intersection of AB' and A'B.

Two fixed points A and B are taken on the coordinates axes such that O A=a and O B=b . Two variable points A ' and B ' are taken on the same axes such that O A^(prime)+O B^(prime)=O A+O Bdot Find the locus of the point of intersection of A B^(prime) and A^(prime)Bdot

Two variable chords A Ba n dB C of a circle x^2+y^2=r^2 are such that A B=B C=r . Find the locus of the point of intersection of tangents at Aa n dCdot

Given x/a+y/b=1 and ax + by =1 are two variable lines, 'a' and 'b' being the parameters connected by the relation a^2 + b^2 = ab . The locus of the point of intersection has the equation

Let A(2,3) and B(2,-4) be two points. If P lie on the x - axis , such that AP = (3)/(7)AB , Find the coordinate of P.

Given that A(1,1) and B(2,-3) are two points and D is a point on A B produced such that A D=3A Bdot Find the coordinates of Ddot

The straight line cuts the coordinate axes at A and B. if the mid point of AB is (3,2) the find the equation of AB.

A straight rod of length 8 units slides with its ends A and B always on the x and y axes respectively. Find the locus of the mid point of the line segment AB.

Two variable chords AB and BC of a circle x^(2)+y^(2)=a^(2) are such that AB=BC=a . M and N are the midpoints of AB and BC, respectively, such that the line joining MN intersects the circles at P and Q, where P is closer to AB and O is the center of the circle. The locus of the points of intersection of tangents at A and C is

A variable line through the point P(2,1) meets the axes at Aa n dB . Find the locus of the centroid of triangle O A B (where O is the origin).