Find the area of the region bounded by the curve $(y - 1)^2 = 4(x + 1)$ and the line $y = (x - 1)$.

Find the area of the region bounded by the curve ( – Class 12 Mathematics

Miscellaneous Exercise 5(II) · Q50

(y - 1)^2 = 4(x + 1)

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From the line, $x=y+1$ . From the parabola, $x=\frac{(y-1)^2}{4}-1$ . Setting them equal: $y+1 = \frac{(y-1)^2}{4}-1 \Rightarrow 4y+4=(y-1)^2-4 \Rightarrow (y-1)^2-4y-8=0 \Rightarrow y^2-6y-7=0 \Rightarrow (y-7)(y+1)=0 \Rightarrow y=7 \text{ or } y=-1$ . Between these, the line's $x$ -value exceeds the parabola's $x$ -value (checked at $y=3$ : line gives $4$ , parabola gives $0$ ). So …

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Q.Find the area of the region bounded by the curve $(y - 1)^2 = 4(x + 1)$ and the line $y = (x - 1)$ .

Concept understanding — Area between Two Curves

Q.Find the area of the region bounded by the curve (y−1)2=4(x+1)(y - 1)^2 = 4(x + 1)(y−1)2=4(x+1) and the line y=(x−1)y = (x - 1)y=(x−1).

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Q.Find the area of the region bounded by the curve $(y - 1)^2 = 4(x + 1)$ and the line $y = (x - 1)$ .

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