Area Under the Curve
Area between Parabola and Line
nta_pyq_2023_jan
Grade 12
Question:
The area enclosed by the curves $y^2+4x=4$ and $y-2x=2$ is:
\dfrac{25}{3}
\dfrac{22}{3}
9
\dfrac{23}{3}
Step-by-Step Solution
Key Concept: Rewrite: $y^2=-4(x-1)$, a leftward parabola with vertex $(1,0)$. Line: $x=\frac{y-2}{2}$. Find intersections: $y=2$ and $y=-4$. Integrate w.r.t. $y$.
Area $=9$.
Correct Answer: 3