Question

find the coordinates of the centre and the radius of the circle. X+2y+2z =15, x^2+y^2+z-2y-4z=11.
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Answer 1

Answer:

7 I think

Step-by-step explanation:

Given equation of sphere is

x

2

+y

2

+z

2

−2y+4z=11

Centre of sphere=(0,1,2)

and radius at sphere =4

Let centre of circle be (α,β,γ)

The direction ratio's of line joining from centre of sphere to the centre of circle is (α−0,β−1,γ−2) or (α,β−1,γ−2)

But this line is normal at plane x+2y+2z=15

∴

1

α

=

2

β−1

=

2

γ−2

=k

⇒α=k,β=2k+1,γ=2k+2

∵ Centre of circle lies on x+2y+2z=15

∴k+2(2k+1)+2(2k+2)=15⇒k=1

So, centre of circle =(1,3,4)

Therefore, radius of circle

(Radius of sphere)

2

−(Length of the line joining centre of the circle and sphere)

2

=

(4)

2

−[(1−0)

2

+(3−1)

2

+(4−2)

2

]

=

7