Question

Find he equation of the tenant plains of the sphere x^2 + y^2 + z^2- 2x + 4y - 6z + 30 =0 Woh are parallel 2x-y + z=0​

Answer 1

2x+2y−z+(1±35)=0.

Any plane parallel to the given plane is

2x+2y−z+λ=0  ...(1)

If it is a tangent plane then perpendicular from centre (0,1,3) should be equal to radius (0+1+9−5)=5.

∴4+4+10+2.1−3+λ=±5

∴λ=1±35

Hence, the required tangent planes are

2x+2y−z+(1±35)=0.