Question

Examine which of the following conicoids are central and which are non-central. Also determine which of the central conicoids have centre at the origin.

(i) x² + y² + z² + 4x + 3y – z = 0

(ii) 2x2-y2z2 + xy + yz - zx = 1

(iii) x2 + y2 - z2 -2xy -3yz - 6zx + x - 2y + 5z + 4 = 0

17 Feb 2025
Answer :
Word Count : 468
To determine which of the given conicoids are central and which are non-central, and to identify if the central conicoids have their center at the origin, we will analyze the equations using the general form of a conicoid and apply the properties related to their center. ### (i) \( x^2 + y^2 + z^2 + 4x + 3y - z = 0 \) Step 1: Completing the square for each variable - For \( x^2 + 4x \), __________ _________ ____ _________ _____ ________ _________ __________.
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