If a circle of constant radius `3k` passes through the origin `O` and meets the coordinate axes at `Aa n dB` , then the locus of the centroud of triangle `O A B` is (a)`x^2+y^2=(2k)^2` (b)`x^2+y^2=(3k)^2` (c)`x^2+y^2=(4k)^2` (d) `x^2+y^2=(6k)^2`

A sphere of constant radius k , passes through the origin and meets the axes at A ,Ba n d Cdot Prove that the centroid of triangle A B C lies on the sphere 9(x^2+y^2+z^2)=4k^2dot

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 sphere of constant radius 2k passes through the origin and meets the axes in A ,B ,a n dCdot The locus of a centroid of the tetrahedron O A B C is a. x^2+y^2+z^2=4k^2 b. x^2+y^2+z^2=k^2 c. 2(x^2+y^2+z)^2=k^2 d. none of these

A sphere of constant radius 2k passes through the origin and meets the axes in A ,B ,a n dCdot The locus of a centroid of the tetrahedron O A B C is a. x^2+y^2+z^2=4k^2 b. x^2+y^2+z^2=k^2 c. 2(x^2+y^2+z)^2=k^2 d. none of these

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

A circle of constant radius a passes through the origin O and cuts the axes of coordinates at points P and Q . Then the equation of the locus of the foot of perpendicular from O to P Q is (A) (x^2+y^2)(1/(x^2)+1/(y^2))=4a^2 (B) (x^2+y^2)^2(1/(x^2)+1/(y^2))=a^2 (C) (x^2+y^2)^2(1/(x^2)+1/(y^2))=4a^2 (D) (x^2+y^2)(1/(x^2)+1/(y^2))=a^2

If a circle passes through the point (a,b) and cuts the circle x^2+y^2=k^2 orthogonally then the locus of its centre is

The tangent at the point P on the rectangular hyperbola x y=k^2 with C intersects the coordinate axes at Qa n dR . Locus of the circumcentre of triangle C Q R is (a) x^2+y^2=2k^2 (b) x^2+y^2=k^2 (c) x y=k^2 (d) None of these

If a circle passes through the points where the lines 3kx- 2y-1 = 0 and 4x-3y + 2 = 0 meet the coordinate axes then k=

If a circle passes through the point (a, b) and cuts the circle x^2 +y^2=k^2 orthogonally, then the equation of the locus of its center is