find the enveloping cylinder of the sphere x^2+y^2+z^2-2x+4y=1 having its generators parallel to x=y=z and also find the guiding curve
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A) Find the enveloping cylinder of the sphere x^(2)+y^(2)+z^(2)-2x+4y-1=0 having its generators ... Also find its guiding curve. ... If the plane 2x-y+z=0 is parallel to the line
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from the given line u have to find the direction cosines (l,m,n)
and the find the values of U V W
From the given sphere equation
now use the U V and W
obtain radius of the sphere ie., a
a=√(U²+V²+W²-d)
substitute all the values in the formula
(x+u)²+(y+v)²+(z+w)²=
[ {l(x-u)+m(y+v)+n(z+w)}²/l²+m²+n²]+a²
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