If a variable plane, at a distance of 3 units from the origin, intersects the coordinate axes at A, B and C, then the locus of the centroid of Δ ABC is :

Question

If a variable plane, at a distance of 3 units from the origin, intersects the coordinate axes at A, B and C, then the locus of the centroid of Δ ABC is : (A) (1/x2) + (1/y2 ) + (1/z2) = 1  (B) (1/x2) + (1/y2 ) + (1/z2) = 3  (C) (1/x2) + (1/y2 ) + (1/z2) = (1/9)  (D) (1/x2) + (1/y2 ) + (1/z2) = 9

Tardigrade Admin · Accepted Answer

Let Centroid be ( h , k , l ) ∴ x - intp =3 h Y -intp =3 k , 3 -int =3 l Equ. (x/3 h)+(y/3 k)+(z/3 ℓ)=1 dist from (0,0,0) |(-1/√(1)9 h2+(1)9 k2+(1/.9|2)|=3 (1/x2)+(1/y2)+(1/z2)=1

Q. If a variable plane, at a distance of $3$ units from the origin, intersects the coordinate axes at $A, B$ and $C$ , then the locus of the centroid of $Δ$ ABC is :

$\frac{1}{x ^{2}} + \frac{1}{y ^{2}} + \frac{1}{z ^{2}} = 1$

$\frac{1}{x ^{2}} + \frac{1}{y ^{2}} + \frac{1}{z ^{2}} = 3$

$\frac{1}{x ^{2}} + \frac{1}{y ^{2}} + \frac{1}{z ^{2}} = \frac{1}{9}$

$\frac{1}{x ^{2}} + \frac{1}{y ^{2}} + \frac{1}{z ^{2}} = 9$

Q. If a variable plane, at a distance of 3 units from the origin, intersects the coordinate axes at A,B and C, then the locus of the centroid of ΔABC is :

x21​+y21​+z21​=1

x21​+y21​+z21​=3

x21​+y21​+z21​=91​

x21​+y21​+z21​=9

Let Centroid be (h,k,l) ∴x− intp =3hY -intp =3k,3 -int =3l Equ. 3hx​+3ky​+3ℓz​=1 dist from (0,0,0) ∣∣​9h21​+9k21​+9∣21​​−1​∣∣​=3 x21​+y21​+z21​=1

Q. If a variable plane, at a distance of $3$ units from the origin, intersects the coordinate axes at $A, B$ and $C$ , then the locus of the centroid of $Δ$ ABC is :

$\frac{1}{x ^{2}} + \frac{1}{y ^{2}} + \frac{1}{z ^{2}} = 1$

$\frac{1}{x ^{2}} + \frac{1}{y ^{2}} + \frac{1}{z ^{2}} = 3$

$\frac{1}{x ^{2}} + \frac{1}{y ^{2}} + \frac{1}{z ^{2}} = \frac{1}{9}$

$\frac{1}{x ^{2}} + \frac{1}{y ^{2}} + \frac{1}{z ^{2}} = 9$