1
Question
A sphere with centre (2,3,0) and radius 1 is drawn in the plane z = 0, equation of the sphere which passes through this sphere and through the point (1,1,1) is
A sphere with centre (2,3,0) and radius 1 is drawn in the plane z = 0, equation of the sphere which passes through this sphere and through the point (1,1,1) is
Open in App
Solution
The correct option is C x2+y2+z2−4x−6y−5z+12=0
Equation of sphere with radius 1 and centre (2,3,0) is given by, (x−2)2+(y−3)2+z2=1
Now required sphere passing through above sphere is given by, (x−2)2+(y−3)2+z2−1+λz=0.
Also it passes through (1,1,1) ⇒1+4+1−1+λ=0⇒λ=−5
Hence, the sphere is x2+y2+z2−4x−6y−5z+12=0
Equation of sphere with radius 1 and centre (2,3,0) is given by,
(x−2)2+(y−3)2+z2=1
Now required sphere passing through above sphere is given by, (x−2)2+(y−3)2+z2−1+λz=0.
Also it passes through (1,1,1) ⇒1+4+1−1+λ=0⇒λ=−5
Hence, the sphere is x2+y2+z2−4x−6y−5z+12=0
Now required sphere passing through above sphere is given by, (x−2)2+(y−3)2+z2−1+λz=0.
Also it passes through (1,1,1) ⇒1+4+1−1+λ=0⇒λ=−5
Hence, the sphere is x2+y2+z2−4x−6y−5z+12=0
Suggest Corrections
0
Similar questions
View More
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program
