Verified Solution • 2025–26 Session moderate

QJEEM21Maaabe: JEE Main 2021 Mathematics - Class 11 JEEM21Maaabe Solution: If x 2 + 9y 2 − 4x + 3 = 0, x, y ∈ R, then x and y respectively …

If x2 + 9y2 − 4x + 3 = 0, x, y ∈ R, then x and y respectively lie in the intervals :

Multiple Choice Options

  • A [−13,13] and [−13,13]
  • B [−13,13] and [1, 3]
  • C [1, 3] and [1, 3]
  • D [1, 3] and [−13,13]

Step-by-Step Verified Solution

x2 + 9y2 − 4x + 3 = 0

(x2 − 4x) + (9y2) + 3 = 0

(x2 − 4x + 4) + (9y2) + 3 − 4 = 0

(x − 2)2 + (3y)2 = 1

(x−2)2(1)2+y2(13)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 y∈[−13,13]

x ∈ [1, 3] y∈[−13,13]

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