Question

Find the equation of the sphere through the
circle x2 + y2 + 2 = 1, 2x + 4y + 5z = 6 and
touching the plane z=0.​

Answer 1

Step-by-step explanation:

general equation of sphere,

x

2

+y

2

+2gx+2fy+2hz+c=0

centre (−g,−f.−h) and radius =

g

2

+f

2

+h

2

−c

At z=0, x

2

+y

2

+2gx+2fy+c=0−−−(i)

x

2

+y

2

−4=0−−−(ii)

comparing (i) and (ii), g=0,f=0,c=−4

∴ general equation reduces to,

x

2

+y

2

+z

2

+2hz+4=0 centre (0,0,h), radius=

h

2

−c

from fig., P is perpendicular drawn from centre to plane and r is radius of sphere. ∴p

2

+9=r

2

9

4h

2

+9=h

2

+4

⇒h=±3

∴ equation of spheres are,

x

2

+y

2

+z

2

+6z−4=0 and x

2

+y

2

+z

2

+6z−4=0