Question

find the equation of the sphere which passes through the circle x²+z²-2x+2z=2, y=0 and touch the plane y-z=7.​

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