If x 2 + 9y 2 − 4x + 3 = 0, x, y ∈ R, then and respectively…

Maths Conic Sections JEE Main 2021 - ( Ellipse ) Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

If x 2 + 9y 2 − 4x + 3 = 0, x, y ∈ R, then and respectively lie in the intervals:

and

and [1,3]

[1,3] and [1,3]

[1,3] and

Text Solution

Verified by Experts

The correct answer is:

x 2 + 9y 2 − 4x + 3 = 0

(x 2 − 4x) + (9y 2 ) + 3 = 0

(x 2 − 4x + 4) + (9y 2 ) + 3 − 4 = 0

(x − 2) 2 + (3y) 2 = 1

(equation of an ellipse).

As it is equation of an ellipse, x\&y can vary inside the ellipse.

So, x − 2 ∈ [−1, 1] and

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