Coordinate Geometry
Ellipse & Line
MMTS_Full_Test_17
Grade 12

Question:

The area of smaller region bounded by the curve $9x^2+4y^2-36x+16y+16=0$ and the line $3x+2y=8$ is
$\dfrac{3}{2}(\pi+2)$
$3(\pi-2)$
$\dfrac{3}{4}(\pi-2)$
$\dfrac{3}{2}(\pi-2)$

Step-by-Step Solution

Key Concept: Rewrite ellipse in standard form; integrate the bounded area
The ellipse becomes $\frac{(x-2)^2}{4}+\frac{(y+2)^2}{9}=1$. Line and ellipse intersection gives area $=\frac{3}{2}(\pi-2)$.
Correct Answer: 4

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