Question

find the equation of the sphere whose center is (1,0,-1) and which passes through the point (2,-1,1)

Answer 1

hey mate
here's the solution

Answer 2

❏QuesTion:-

$\sf \red{Find \: the \: equation \: of \: the \: sphere \: whose} \\ \green{\sf centre \: is \: (1, 0, - 1) \: and \: which \: passes } \\ \purple{ \sf through \: the point</p><p>(2 - 1, 1)}$

❏Answer :-

$\green{\boxed{\sf \red{ \star } \orange{ {(x - 1)}^{2} }+ \red{{y}^{2} + } \pink{{(z + 1)}^{2} } = 6}} \: \\ \sf or \: \red{ you \: can \: minimize \: it \: by \: opening} \\ \sf \: whole \: square$

❏To Find :-

→ Equation of sphere .

❏SoluTion :-

$\sf \blue{ consider \: an \: eqation \: of \: sphere \:} \\ \sf whose \: centre \: is(a , b, c) \: and \: passing \\ \sf \orange{ through \: the \: points \: (l, m, n)} \: with \: \\ \sf radius \: r. \\ \\ \to \sf {(x - a)}^{2} + {(y - b)}^{2} + {(z - c)}^{2} = {r}^{2} \\ \\ \sf \: therefore \\ \sf \blue{ we \: have} \\ \star \sf (a , b, c) \: \leadsto \green{ (1 , 0, - 1) }\\ \star \orange{ \sf(l, m, n) \leadsto} \: (2 , - 1, 1) \\ \therefore \\ \\ \to \sf \red{{(x - 1)}^{2} } + \green{ {(y - 0)}^{2}} + \pink{{(z + 1)}^{2}} = {r}^{2} \\ \bf \orange{passing \: through }\: (2 , - 1, 1) \\ \\ \to \sf \blue{ {(2 - 1)}^{2} + } \green{ {( - 1 - 0)}^{2} + } \purple{ {(1 + 1)}^{2} = {r}^{2} }\\ \\ \to \sf1 + \red{ 1+ 4 = } {r}^{2} \\ \\ \to \boxed{ \sf r = \green{ \sqrt{ \pink{6}}} } \\ \\ \sf hence \: \red{ equation} \: of \: sphere \: \red{ is }\\ \\( \because \sf {r}^{2} = 6) \\ \green{\boxed{\sf \red{ \star } \orange{ {(x - 1)}^{2} }+ \red{{y}^{2} + } \pink{{(z + 1)}^{2} } = 6}}$

Hope it helps you .