Coordinate Geometry
Area of region defined by inequalities
MMTS_Full_Test_04
Grade 12
Question:
Let $S=\{(x,y)\in\mathbb{R}\times\mathbb{R}: y^2\leq8x,\;y^2\geq32-8x,\;x+y-6\geq0,\;4x-3y-8\leq0,\;x\geq0,\;y\geq0\}$. If area $=A$, value of $21A+792$ is
(A) 2024
(B) 1012
(C) 1000
(D) 343
Step-by-Step Solution
Key Concept: Find vertices of region $S$ by intersecting boundaries. Compute area by integration or shoelace.
$21A+792=1000$.
Correct Answer: (C) 1000