Home
Class 12
MATHS
A variable plane is at a constant distan...

A variable plane is at a constant distance k from the origin and meets the coordinate axes at A, B, C. Then the locus of the centroid of the triangle ABC is

A

`x^(-2)+y^(-2)+z^(-2)=k^(-2)`

B

`x^(-2)+y^(-2)+z^(-2)=4k^(-2)`

C

`x^(-2)+y^(-2)+z^(-2)=16k^(-2)`

D

`x^(-2)+y^(-2)+z^(-2)=9k^(-2)`

Text Solution

Verified by Experts

The correct Answer is:
(d)
Promotional Banner

Similar Questions

Explore conceptually related problems

A line is at a constant distance c from the origin and meets the coordinate axes in A and B . The locus of the centre of the circle passing through O, A, B is

If the plane 3x+4y-3z+2=0 cuts the coordinate axes at A, B, C, then the centroid of the triangle ABC is

If a circle of constant radius 3k passes through the origin and meets the axes in A and B, then the locus of the centroid of triangleOAB is :

The plane ax + by + cz = 1 meets the coordinate axes in A, B, C. The centroid of the triangle is :

If the plane 7x+11y+13z=3003 meets the axes A, B, C then the centroid of the triangle ABC is

A variable plane at a distance of 1 unit from the origin cuts the coordinate axes at A,B and C satisfies the relation 1/x^2+1/y^2+1/z^2= k , then the value of k is :

The plane x/4 + y/3 -z/5 =1 cuts the axes at A, B, C then the area of the triangle ABC is

The tangent to the curve xy = 25 at any point on it cuts the coordinate axes at A and B , then the area of the triangle OAB is

A plane meets the coordinate axes at A, B, C such that the centroid of the triangle ABC is (3,4,5). Then the equation of the plane is

A plane meets the coordinate axes at A, B, C such that the centroid of the triangle is (3, 3, 3). The equation of the plane is :