Question

The centre of sphere passes through four points (0, 0, 0),

(0, 2, 0), (1, 0, 0) and (0, 0, 4) is

s

• A. $\left( \frac{1}{2},1,2 \right)$
• B. $\left( - \frac{1}{2},1,2 \right)$
• C. $\left( \frac{1}{2},1, - 2 \right)$
• D. $\left( 1,\frac{1}{2},2 \right)$

Answer 1

Answer: (A)

$\left( \frac{1}{2},1,2 \right)$

Answer 2

Let the equation of sphere

$x ^ { 2 } + y ^ { 2 } + z ^ { 2 } + 2 u x + 2 v y + 2 w z + d = 0$

$\bullet \bullet$ It passes through origin (0, 0, 0),

∴ $d = 0$

Also, it passes through (0, 2, 0)

∴ $4 + 4 v = 0 \Rightarrow v = - 1$

Also, it passes through (1, 0, 0)

∴ $1 + 2 u = 0 \Rightarrow u = - 1 / 2$

And it passes through (0, 0, 4)

∴ $16 + 8 w \Rightarrow w = - 2$

∴ Centre $( - u , - v , - w ) = \left( \frac { 1 } { 2 } , 1,2 \right)$.