Question

Find the equation of the right circular cylinder which envelops a sphere of centre
(a, b, c) and radius r and has its generators parallel to the direction <1, m, n >
​

Answer 1

Answer:

envelops a sphere of centre (a,b,c) and radius R and has its generators parallel to a ... apoint P(p,q,r) from a line through A(a,b,c) and whose direction cosine are l,m,n is (A)

Answer 2

Answer:

The Equation of cylinder is,

[(x-a)² + (y-b)² + (z-c)² - r² ] ( l² + m² + n² ) = [ l (x-a) + m(y-b) + n (z-c) ]²

Step-by-step explanation:

Solution,

Given,

Radius = r

sphere of centre = a, b, c

Equation to the axis of the cylinder passes through (a,b,c)

Hence equation to the axis is

$\frac{x-a}{l} = \frac{y-b}{m} = \frac{z-c}{n}$

Equation of the right circular cylinder which envelops a sphere of centre (a,b,c) and radius r and has its generators parallel to the direction l,m,n is given by,

[(x-a)² + (y-b)² + (z-c)² - r² ] ( l² + m² + n² ) = [ l (x-a) + m(y-b) + n (z-c) ]²

∦SPJ3