Question

Find the centre and radius of the sphere
${x }^{2} + {y}^{2} + {z}^{2} - 4x + 6y - 8z = 71$
​

Answer 1

Step-by-step explanation:

General equation of the circle is (x−a) 2+(y−b) 2+(z−c) 2

=r 2

where (a,b,c) is center of circle and r is radius of circle.

So, x

2 +y 2 +z 2 −4x+6y−8z−7=0 can be written as

(x 2 −2×2x+2 2 )+(y 2+2×3y+3 2 )+(z 2 −2×4z+4 2 )−2 2 −3 2 −4 2 −7=0

⇒(x−2) 2 +(y+3) 2+(z−4) 2

=4+9+16+7=36

⇒(x−2) 2 +(y+3) 2+(z−4) 2=6 2

Which is the equation of sphere with center (2,−3,4) and radius 6 unit.

Thus, the diameter is 12 units.