Question

The equation x²+y²-az²-2x+6y-4z+2=0
Represents a sphere for​

Answer 1

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.