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 and B are two variable points on x, y axes respectively such that OA+OB=c . The locus of the foot of the perpendicular from origin on this line overset(" "harr)("AB") is

A plane passes through a fixed point (a ,b ,c)dot Show that the locus of the foot of the perpendicular to it from the origin is the sphere x^2+y^2+z^2-a x-b y-c z=0.

A plane passes through a fixed point (a ,b ,c)dot Show that the locus of the foot of the perpendicular to it from the origin is the sphere x^2+y^2+z^2-a x-b y-c z=0.

A plane passes through a fixed point (a ,b ,c)dot Show that the locus of the foot of the perpendicular to it from the origin is the sphere x^2+y^2+z^2-a x-b y-c z=0.

A plane passes through a fixed point (a ,b ,c)dot Show that the locus of the foot of the perpendicular to it from the origin is the sphere x^2+y^2+z^2-a x-b y-c z=0.

A and B are two points on the x-axis and y-axis respectively. P(2, -3) is the mid point of AB. Find the slope of line AB

A and B are two points on the x-axis and y-axis respectively. P(2, -3) is the mid point of AB. Find the equation of line AB.

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) .

If A,B are the feet of the perpendicular from P (2,4,5) to the x-axis and y-axis respectively, then AB =