Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

JEE Main 202623 JanuaryEvening Shift

Exam: JEE Main
Year: 2026
Date: 23 January
Shift: Evening Shift
Subject: Mathematics
Chapter: Area Under Curves

JEE Main 2026 · 23 January · Evening Shift · Mathematics · Area Under Curves

The area of the region enclosed between the circles x^ 2 +y^ 2 =4...

The area of the region enclosed between the circles

x^{2}+y^{2}=4

and

x^{2}+(y-2)^{2}=4

is:

Options

A $\frac{4}{3}(2 \pi-3 \sqrt{3})$
B $\frac{2}{3}(2 \pi-3 \sqrt{3})$
C $\frac{2}{3}(4 \pi-3 \sqrt{3})$
D $\frac{4}{3}(2 \pi-\sqrt{3})$

Correct answer

C. $\frac{2}{3}(4 \pi-3 \sqrt{3})$

Step-by-step solution

Circle 1: centre

(0,0)

,

r=2

. Circle 2: centre

(0,2)

,

r=2

. Distance between centres

d=2

.
Intersection:

y^2 = (y-2)^2 \Rightarrow y = 1

, giving

x = \pm\sqrt{3}

.
Angle subtended at centre of circle 1 by the chord:

\theta = 2\pi/3

.
Segment area

= \frac{1}{2}(4)\left(\frac{2\pi}{3}\right) - \frac{1}{2}(4)\sin\frac{2\pi}{3} = \frac{4\pi}{3} - \sqrt{3}

.
By symmetry, total intersection area

= 2\left(\frac{4\pi}{3} - \sqrt{3}\right) = \frac{8\pi - 6\sqrt{3}}{3} = \frac{2}{3}(4\pi - 3\sqrt{3})

.

Practice Area Under Curves on Quantrex Academy →

More from Area Under Curves

Passage: Consider the curve C_1 given by y = e^ -x for x ∈ [0, 10π] , and the curve C_2… JEE Advanced 2026 Passage: Consider the ellipses given by x^2 + 4y^2 = 1 and 4x^2 + y^2 = 1 . Question: If… JEE Advanced 2026 The area of the region \ (x, y) : x^2 - 8x ≤ y ≤ -x\ is : JEE Main 2026 The area of the region \ (x, y) : 0 ≤ y ≤ 6 - x, y^2 ≥ 4x - 3, x ≥ 0\ is: JEE Main 2026 The area of the region R = \ (x, y): xy ≤ 27, 1 ≤ y ≤ x^2\ is equal to: JEE Main 2026 The area of the region bounded by the curves x+3y^2=0 and x+4y^2=1 is equal to: JEE Main 2026 The area of the region \ (x, y): y ≤ π - |x|, y ≤ |x x|, y ≥ 0\ is: JEE Main 2026 If the area of the region bounded by 16x^2 - 9y^2 = 144 and 8x - 3y = 24 is A, then 3(A +… JEE Main 2026 Let P_ 1 : y=4 x^ 2 and P_ 2 : y=x^ 2 +27 be two parabolas. If the area of the bounded… JEE Main 2026 The area of the region R=\ (x, y): x y ≤ 8,1 ≤ y ≤ x^ 2 , x ≥ 0\ is JEE Main 2026 Let f(α) denote the area of the region in the first quadrant bounded by x=0, x=1, y^ 2 =x… JEE Main 2026 Let A_ 1 be the bounded area enclosed by the curves y=x^ 2 +2, x+y=8 and y -axis that… JEE Main 2026 Let the area of the region bounded by the curve y= \ x, x\ , lines x=0, x=(3 π)/(2) , and… JEE Main 2026 The area of the region A=\ (x, y): 4 x^ 2 +y^ 2 8. and .y^ 2 4 x\ is: JEE Main 2026 Let the line x=-1 divide the area of the region \ (x, y): 1+x^ 2 ≤ y ≤ 3-x\ in the ratio… JEE Main 2026 If the area of the region \ (x, y): 1-2 x y 4-x^ 2 , x 0, y 0\ is (α)/(β), α, β ∈ N, (α… JEE Main 2026 Full Area Under Curves list Area Under Curves JEE Maths PYQs JEE Mathematics PYQs All JEE Main PYQs