Home
Class 12
MATHS
A variable plane which remains at a con...

A variable plane which remains at a constant distance P from the origin (0) cuts the coordinate axes in A, B and C

A

Locus of centroid of tetrahedron OABC is `x ^(2) y ^(2) +y ^(2) z^(2) + z ^(2) x ^(2) = (16)/(p ^(2)) x ^(2) y ^(2) z ^(2)`

B

Locus of centroid of tetrahedron OABC is `x ^(2) y ^(2) + y ^(2) z ^(2) + z ^(2) x ^(2) = (4)/(p ^(2))x ^(2)y^(2) z^(2)`

C

Parametric equation of the centroid of the tetrahedron is of the form `((p)/(4)sec alpha sec beta, (p)/(4) sec alpha cosec beta, (p)/(4) cos ec alpha ),alpha, beta in 0, 2pi)-pi//2,pi,3pi //2)`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
A, C
Promotional Banner

Similar Questions

Explore conceptually related problems

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

(i) A variable plane, which remains at a constant distance '3p' from the origin cuts the co-ordinate axes at A, B, C. Show that the locus of the centroid of the triangle ABC is : (1)/(x^(2)) + (1)/(y^(2)) + (1)/(z^(2)) = (1)/(p^(2)) . (ii) A variable is at a constant distance 'p' from the origin and meets the axes in A, B, C respectively, then show that locus of the centroid of th triangle ABC is : (1)/(x^(2)) + (1)/(y^(2)) + (1)/(z^(2)) = (9)/(p^(2)).

A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A,B,C. Show that the locus of the centroid of triangle ABC is (1)/(x^(2))+(1)/(y^(2))+(1)/(z^(2))=(1)/(p^(2))

A variable plane which remains at a constant distance p from the origin cuts coordinate axes in A,B,C.sof centroid of tetrahedron OABC is y^(2)z^(2)+z^(2)x^(2)+x^(2)y^(2)=kx^(2)y^(2)z^(2) where k is equal to

If a variable plane which is at a constant distance 3p from the origin cut the co-ordinate axes at points A ,B , C , then locus of the centroid of DeltaABC is

A variable plane is at a constant distance 3p from the origin and meets the coordinates axes in A,B and C if the centroid of triangle ABC is (alpha,beta,gamma ) then show that alpha^(-2)+beta^(-2)+gamma^(-2)=p^(-2)

A variable plane is at a constant distance p from the origin and meets the coordinate axes in A,B,C .Show that the locus of the centroid of the tehrahedron OABCisx^(-2)+y^(-2)+z^(-2)=16p^(-2)

A variable plane at a constant distance p from the origin meets the coordinate axes in points A,B and C respectively.Through these points, planes are drawn parallel to the coordinate planes,show that locus of the point of intersection is (1)/(x^(2))+(1)/(y^(2))+(1)/(z^(2))=(1)/(p^(2))