Question

Find the condition that the plane Ix+my+nz = p may touch the paraboloid ax² +by² = 2 cz. Find also the Co-ordinates of the point of contact.​

Answer 1

Answer:

Correct option is

C

l

2

+m

2

+n

2

If line lx+my+nz=p touches the sphere x

2

+y

2

+z

2

+2ux+2vy+2wz+d=0, then distance of line from centre of the sphere is same as its radius.

⇒

∣

∣

∣

∣

∣

l

2

+m

2

+n

2

−lu−mv−nw−p

∣

∣

∣

∣

∣

=

u

2

+v

2

+w

2

−d

⇒(lu+mv+nw+p)

2

=(l

2

+m

2

+n

2

)(u

2

+v

2

+w

2

−d)

Comparing it with (lu+mv+nw+p)

2

=k(u

2

+v

2

+w

2

−d), we get k=l

2

+m

2

+n

2

Answer 2

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