A circle of radius r passes through the origin and intersects the x-axis and y-axis at P and Q respectively. Show that the equation to the locus of the foot of the perpendicular drawn form the origin upon the line segment `bar (PQ)` is `(x^(2)+y^(2))^(3)=4r^(2)x^(2)y^(2)`.

A circle of constant radius r passes through the origin O and cuts the axes at A and B. Show that the locus of the foot of the perpendicular from O to AB is (x^2+y^2)^2(x^(-2)+y^(-2))=4r^2 .

A circle of constant radius r passes through the origin O and cuts the axes at A and B. Show that the locus of the foot of the perpendicular from O to AB is (x^2+y^2)^2(x^(-2)+y^(-2))=4r^2 .

A circle of radius r passes through origin and cut the x-axis and y-axis at P and Q . The locus of foot of perpendicular drawn from origin upon line joining the points P and Q is (A) (x^2+y^2)^3=r^2(x^2y^2) (B) (x^2+y^2)^2(x+y)=r^2(xy) (C) (x^2+y^2)^2=r^2(x^2y^2) (D) (x^2+y^2)^3=4r^2(x^2y^2)

A line passing through the point P(4,2) meets the x and y-axis at A and B respectively. If O is the origin, then locus of the centre of the circumcircle of triangle OAB is

A circle of radius r passes through origin and cut the y-axis at P and Q. The locus of foot of perpendicular drawn from origin upon line joining the points P and Q is (A) (x^(2)+y^(2))^(3)=r^(2)(x^(2)y^(2))(B)(x^(2)+y^(2))^(2)(x+y)=r^(2)(xy)(C)(x^(2)+y^(2))^(2)=r^(2)(x^(2)y^(2))(D)(x^(2)+y^(2))^(3)=4r^(2)(x^(2)y^(2))

A line passing through P(4, 2) meets the x and y-axis at A and B respectively. If O is the origin, then locus of the centre of the circumcircle of DeltaOAB is :

Two points A and B move on the positive direction of x-axis and y-axis respectively, such that OA + OB K. Show that the locus of the foot of the perpendicular from the origin O on the line ABís (x + y)(x2 + y2) = Kxy. · (0,b)B Let the equation of AB be =1 a

A circle of constant radius r passes through the origin O, and cuts the axes at A and B. The locus of the foots the perpendicular from O to AB is (x^(2) + y^(2)) =4r^(2)x^(2)y^(2) , Then the value of k is

A circle of constant radius r passes through the origin O, and cuts the axes at A and B. The locus of the foots the perpendicular from O to AB is (x^(2) + y^(2))^k =4r^(2)x^(2)y^(2) , Then the value of k is

Find the equation of a circle which passes through the origin and makes intercepts of 2 units and 4 units on x-axis and y-axis respectively.