The area enclosed by the curves |y +x| ≤ 1, |y-x| ≤ 1 and 2 x2+2 yy=1 is

Question

The area enclosed by the curves |y +x| ≤ 1, |y-x| ≤ 1 and 2 x2+2 yy=1 is (A) (2+(π/2)) sq units (B) (2-(π/2)) sq units (C) (3+(π/2)) sq units (D) (3-(π/4)) sq units

Tardigrade Admin · Accepted Answer

The curves y+x ≤ 1 and |y-x| ≤ 1 form a square A B C D and 2 x2+2 y2=1 is a circle of radius (1/√2) and center (0,0). <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/f465dc7e1ebc81c928b8e42fe2ec1f57-.png" /> ∴ Required Area = Area of square - Area of circle =(2-(π/2)) sq units

Q. The area enclosed by the curves $∣ y + x ∣ \leq 1$ , $∣ y - x ∣ \leq 1$ and $2 x^{2} + 2 y^{y} = 1$ is

$(2 + \frac{π}{2})$ sq units

$(2 - \frac{π}{2})$ sq units

$(3 + \frac{π}{2})$ sq units

$(3 - \frac{π}{4})$ sq units

The curves $y + x \leq 1$ and $∣ y - x ∣ \leq 1$ form a square $A BC D$ and $2 x^{2} + 2 y^{2} = 1$ is a circle of radius $\frac{1}{2}$ and center $(0, 0)$ .

$∴$ Required Area
= Area of square - Area of circle
$= (2 - \frac{π}{2})$ sq units

Q. The area enclosed by the curves ∣y+x∣≤1, ∣y−x∣≤1 and 2x2+2yy=1 is

(2+2π​) sq units

(2−2π​) sq units

(3+2π​) sq units

(3−4π​) sq units