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Match the items of Column I with those of Column II.Column IColumn II(A) The equation of the locus of a point whose distance from the z-axis is equal to its distance from the xy-plane is(p) x2 + y2 + z2 - 6x + 2y - 4z + 5 = 0(B) The equation of the sphere with centre at (3, −1, 2) and touching yz-plane is(q) y2 - 2y - 4x + 4z + 6 = 0(C) The equation of the locus of the point whose distance from (2, −1, 3) is 4 is(s) x2 + y2 - z2 = 0(D) The equation of the locus of the point whose distance from the y-axis is equal to its distance from the point (2, 1, −1) is(t) x2 + y2 + z2 - 4x + 2y - 6z - 2 = 0 |
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Answer» (A) → (s), (B) → (p), (C) → (t), (D) → (q) Explanation : (A) → (s) (A) The distance of a point from z-axis is √(x2 + y2). The distance of the point from xy-plane is |z|. Therefore x2 + y2 = z2 or x2 + y2 − z2 = 0 (B) Since the sphere touches yz-plane, its radius is |x|. Hence, the equation of the sphere is (x - 3)2 + (y + 1)2 + (z - 2)2 = 32 x2 + y2 + z2 - 6x + 2y - 4z + 5 = 0 (C) The locus is (x - 2)2 + (y + 1)2 + (z - 3)2 = 16 x2 + y2 + z2 -4x + 2y - 6z - 2 = 0 (D) We have √(x2 + z2) = √((x - 2)2 + (y - 1)2 + (z + 1)2) x2 + z2 = (x - 2)2 + (y - 1)2 + (z + 1)2 y2 - 4x - 2y + 2z + 6 = 0 |
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