AP EAPCET 24-Aug-2021 Shift 2 Paper

x

a

+

y

b

+

z

c

=1 which is unit distance from the origin cuts the coordinates axes at A, B and C.
∴ 1=

1

√ 1 a2 + 1 b2 + 1 c2

⇒

1

a2

+

1

b2

+

1

c2

=1
Coordinate of vertices of Δ‌ABC is
A(a,0,0),B(0,b,0),C(0,0,c)
∵ Centroid of Δ‌ABC is (

a

3

,

b

3

,

c

3

)
Now, (

a

3

,

b

3

,

c

3

) satisfied the equation

1

x2

+

1

y2

+

1

z2

=k
∴

9

a2

+

9

b2

+

9

c2

=k
9(

1

a2

+

1

b2

+

1

c2

)=k [∵

1

a2

+

1

b2

+

1

c2

=1]
∴ k = 9