A sphere is inscribed in the tetrahedron with faces X=0,y=0,z=0,2x+6y+3z=14.find the equation of sphere
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The equation of the sphere touching co - ordinate planes is x
2
+y
2
+z
2
−2λ(x+y+z)+2λ
2
=0.
Its centre is (λ,λ,λ) and radius λ.
If it touches 2x+6y+3z−14=0; then perpendicular from centre should be equal to radius.
∴
(4+36+9)
2λ+6λ+3λ−14
=λ
∴11λ−14=±7λ
∴λ=
9
7
or
2
7
Centre,radius equation are (
9
7
,
9
7
,
9
7
),
9
7
,81(x
2
+y
2
+z
2
) −126(x+y+z)+98=0 respectively.
(
2
7
,
2
7
,
2
7
),
2
7
,2(x
2
+y
2
+z
2
) +14(x+y+z)+49=0 respectively
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