Let a point P(x, y) is called rational point if x & y both belong to set of rational numbers Column-IColumn-II(i) Number of rational points on the ellipse += 1 is[A] ∞(ii) Number of integral points on the ellipse + = 1 is[Β] 2(iii) Number of rational points on the circle with centre at (π, e) is[C] 4(iv) Number of rational points on the circle with centre at (0, ) is[D]1

Let a point P(x, y) is called rational point if x & y both …

Maths Conic Sections Mix Matrix Match Questions

Published on: August 14, 2026

Let a point P(x, y) is called rational point if x & y both belong to set of rational numbers

Column-I	Column-II
(i) Number of rational points on the ellipse += 1 is	[A] ∞
(ii) Number of integral points on the ellipse + = 1 is	[Β] 2
(iii) Number of rational points on the circle with centre at (π, e) is	[C] 4
(iv) Number of rational points on the circle with centre at (0, ) is	[D]1

Correct Matrix Matching

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The correct answer is:

(i) [A]; (ii) [C]; (iii) [D]; (iv) [B]

Ans.

(i) [A]

(ii) [C]

(iii) [D]

(iv) [B]

Sol.

(i) Let any point on the ellipse is (3 cos θ , 2 sin θ ) which can be rational for a values of θ ∈ [0, 2 π ]

(ii) (± 3, 0) and (0, ± 2) are 4 integral points.

(iii) Do yourself

(iv) Do yourself

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