Question

Find the equation of sphere which passes through the points $(1,-3,4),(1,-5,2),(1,-3,0)$ and whose centre lies on the plane $x+y+z=0$.

• A. $(x+1{)}^2+(y+3{)}^2+(z+2{)}^2=4$
• B. $(x-1{)}^2+(y+3{)}^2+(z-2{)}^2=4$
• C. $(x+1{)}^2+(y-3{)}^2+(z+2{)}^2=4$
• D. $(x-1{)}^2+(y-3{)}^2+(z-2{)}^2=4$

Answer 1

The correct option is B $(x-1{)}^2+(y+3{)}^2+(z-2{)}^2=4$

Let$(h,k,l)$ be the centre.

$\therefore (h-1{)}^2+(k+3{)}^2+(l-4{)}^2=(h-1{)}^2+(k+5{)}^2+(l-2{)}^2---\left(i\right)$

$\therefore (h-1{)}^2+(k+3{)}^2+(l-4{)}^2=(h-1{)}^2+(k+3{)}^2+l^2---(ii)$

From equation $\left(ii\right)$, $l=2$

putting $l=2$ in $\left(i\right)$ and solving, $k=-3$

$h+k+l=0$ $\therefore h=1$ and

radius$=\sqrt{(1-1{)}^2+(-3+3{)}^2+2^2}$

equation of sphere:$(x-1{)}^2+(y+3{)}^2+(z-2{)}^2=4$