Question
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 :
JEE Main
Mathematics
Area Under Curves
2026
JEE Main 2026 (21 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 2 -1
- B. 3( -1)
- C. 2 - 1 2
- D. 2( -1)
Answer
D. 2( -1)
Step-by-step solution
Ellipse: x^2 4 + y^2 = 1 with a = 2, b = 1. Area = ab = 2 . Curves y = |x| - 1 and y = 1 - |x| intersect at x = 1, forming a rhombus with vertices (0, 1), (1, 0), (0, -1), (-1, 0). Vertices (0, 1) lie on ellipse; ( 1, 0) are inside ellipse. Area of rhombus = 1 2 2 2 = 2. Required area = 2 - 2 = 2( - 1).
Related: Mathematics — Area Under Curves · All PYQ Banks