IDZ Ryabushko 4.2 Variant 29
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№1 Reduce the second-order surface equation to canonical form. a) 3x2 - 9y2 + z2 + 27 = 0; b) z2 - 2y = - 4x2.
№2 Write down the equation and determine the type of surface obtained by rotating this line around the specified coordinate axis, make a picture: a) 5y2 - 8z2 = 40; Oz b) y = 3; z is 1; Ox.
№3 Build a body bounded by the indicated surfaces: a) z = 3y2; x2 + y2 = 9; z = 0.
b) x + y + z = 8; x + 2y = 4; x + 4y = 4; y = 0; z = 0.
№2 Write down the equation and determine the type of surface obtained by rotating this line around the specified coordinate axis, make a picture: a) 5y2 - 8z2 = 40; Oz b) y = 3; z is 1; Ox.
№3 Build a body bounded by the indicated surfaces: a) z = 3y2; x2 + y2 = 9; z = 0.
b) x + y + z = 8; x + 2y = 4; x + 4y = 4; y = 0; z = 0.
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