CAT 2024 Inequalities Question (Hard)

Question

In the -plane, the area, in sq. units, of the region defined by the inequalities and is

Accepted Answer

We are to find the area of the region defined by these inequalities 1. 2. --- Step 1 Analyze the second inequality Rewrite x 2 y 2 4x - 4y le 0 quad quad x 2 y 2 4x - 4y ge -4 Convert to circle form Group and x 2 4x y 2 - 4y k quad -4 le k le 0 Complete the square x 2 2 - 4 y-2 2 - 4 k x 2 2 y-2 2 k

CAT 2024

Quantitative

Inequalities

Hard

In the $XY$ -plane, the area, in sq. units, of the region defined by the inequalities $y \geq x + 4$ and $-4 \leq x^2 + y^2 + 4(x - y) \leq 0$ is

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