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JEE Main 202621 JanuaryMorning Shift

Exam: JEE Main
Year: 2026
Date: 21 January
Shift: Morning Shift
Subject: Mathematics
Chapter: Area Under Curves

JEE Main 2026 · 21 January · Morning Shift · Mathematics · Area Under Curves

The area of the region, inside the ellipse x^ 2 +4 y^ 2 =4 and...

The area of the region, inside the ellipse

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

and outside the region bounded by the curves

y=|x|-1

and

y=1-|x|

, is :

Options

A $2 \pi-1$
B $3(\pi-1)$
C $2 \pi-\frac{1}{2}$
D2( $\pi-1$ )

Correct answer

D. 2( $\pi-1$ )

Step-by-step solution

Ellipse:

\frac{x^2}{4} + y^2 = 1

with

a = 2

,

b = 1

. Area

= \pi ab = 2\pi

.
Curves

y = |x| - 1

and

y = 1 - |x|

intersect at

x = \pm 1

, forming a rhombus with vertices

(0, 1)

,

(1, 0)

,

(0, -1)

,

(-1, 0)

.
Vertices

(0, \pm 1)

lie on ellipse;

(\pm 1, 0)

are inside ellipse.
Area of rhombus

= \frac{1}{2} \times 2 \times 2 = 2

.
Required area

= 2\pi - 2 = 2(\pi - 1)

.

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