A variable plane passes through a fixed point `(a ,b ,c)` and cuts the coordinate axes at points `A ,B ,a n dCdot` Show that the locus of the centre of the sphere `O A B Ci s a/x+b/y+c/z=2.`

A plane passes through a fixed point (a, b, c) and cuts the axes in A, B, C. The locus of a point equidistant from origin A, B, C must be

Write the coordinates of the points B marked on the axes in the given figure :

A variable plane is at a distance k from the origin and meets the coordinates axes is A,B,C. Then the locus of the centroid of DeltaABC is

A variable plane which remains at a constant distance p from the origin cuts the coordinate axes in A, B, C. The locus of the centroid of the tetrahedron OABC is x^(2)y^(2)+y^(2)z^(2)+z^(2)x^(2)=(k)/(p^(2))x^(2)y^(2)z^(2), then root(5)(2k) is

If the plane x/2+y/3+z/4=1 cuts the coordinate axes in A, B,C, then the area of triangle ABC is

A plane passing through (1,1,1) cuts positive direction of coordinates axes at A ,Ba n dC , then the volume of tetrahedron O A B C satisfies a. Vlt=9/2 b. Vgeq9/2 c. V=9/2 d. none of these

A variable line passes through a fixed point P. The algebraic sum of the perpendiculars drawn from the points (2, 0), (0, 2) and (1, 1) on the line is zero. Find the coordinates of the point P.

IF a circle passes through the point (0,0) (a,0),(0,b) then find the coordinates of its centre. Thinking process :

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