Question

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

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

• 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 be

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

$\bullet \bullet$ It passes through (0, 0, 0), $\therefore$ $d = 0$

Also, It passes through (0, 2, 0) i.e., $v = - 1$

Also, It passes through (1, 0, 0) i.e., $u = - 1 / 2$

Also, it passes through (0, 0, 4) i.e., $w = - 2$

∴ Centre (–u, –v, –w) = (1/2, 1, 2)