# Find the equation of right circular cylinder whose curve is the circle in #(x+1/2)^2+(y-1)^2+(z+1)^2=21/4# has as center the point #(-1/2,1,-1)#?

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See below.

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**(Sir, actually question is Find the distance of the centre of the circle x²+y²+z²+x-2y+2z=3,2x+y+2z=1 from the plane ax+by+cz=d where a,b,c,d are constant.Also find the equation of right circular cylinder whose base curve is the circle in above.Sir,I need help in solving the second part of this question. on Find the equation of right circular cylinder whose curve is the circle in #(x+1/2)^2+(y-1)^2+(z+1)^2=21/4# has as center the point #(-1/2,1,-1)#?)**

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Giving the circle

with

and

where

determine the right cylinder whose generating curve is

The center of

now the

so the cylinder

Assuming the generating line given by

solving for

but the generating line must be tangent to

Now considering

Attached a plot showing the arrangement.

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