Question

find the circular section of ellipsoid x2+2y2+6z2=28​

Answer 1

Answer:

Step-by-step explanation:

    x² + 2y² + 6z² = 28

   x²/28 + 2y²/28 + 6z²/28 = 28/ 28

   x²/28 + y²/14 + z²/14/3  = 1

x²/28 + y²/14 + z²/14/3 - 1 = 0

s +  У.u. v = 0

where s = 0, represents on sphere and u = 0,  v = 0 are the equation of two  plains

x² + y²  + z². / 28 + y² ( 1/14 - 1/28 ) + z² (3/14 - 1/28) = 0...(2)

The pair of plains given by

y² ( 1/14 - 1/28 ) + z² (3/14 - 1/28) = 0..(3)

meet the clipboard (1) where meet  the sphere given,

x² + y²  + z² = 28   ...(4)

Hence the ellipsoid  1 by the planes given by 2 are circles each of radius √28