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Consider a sphere passing through the origin and the points $(2,1,-1),(1,5,-4),(-2,4,-6)$
Consider the following statements:
1 . The sphere passes through the point $(0,4,0)$.
2 . The point $(1,1,1)$ is at a distance of 5 unit from the centre of the sphere. Which of the above statements is/are correct?
Options:
Consider the following statements:
1 . The sphere passes through the point $(0,4,0)$.
2 . The point $(1,1,1)$ is at a distance of 5 unit from the centre of the sphere. Which of the above statements is/are correct?
Solution:
1402 Upvotes
Verified Answer
The correct answer is:
1 only
(1) Equation of sphere is $x^{2}+y^{2}+z^{2}+2 x-4 y+6 z=0$
Put the value $(0,4,0)$, we get $0+16+0+0-16+0=0$
So, the sphere passes through the point $(0,4,0)$. Hence, Statement 1 is correct.
2 . Distance between the point $(1,1,1)$ and centre of sphere $(-1,2,-3)$
$=\sqrt{(1+1)^{2}+(1-2)^{2}+(1+3)^{2}}$
$=\sqrt{4+1+16}=\sqrt{21} \neq 5$
Hence, statement 2 is not correct.
Put the value $(0,4,0)$, we get $0+16+0+0-16+0=0$
So, the sphere passes through the point $(0,4,0)$. Hence, Statement 1 is correct.
2 . Distance between the point $(1,1,1)$ and centre of sphere $(-1,2,-3)$
$=\sqrt{(1+1)^{2}+(1-2)^{2}+(1+3)^{2}}$
$=\sqrt{4+1+16}=\sqrt{21} \neq 5$
Hence, statement 2 is not correct.
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