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QJEEM21Ma8c03: JEE Main 2021 Mathematics - Class 12 JEEM21Ma8c03 Solution: The area of the region bounded by the parabola (y − 2) 2 = (x − …

The area of the region bounded by the parabola (y

-

2)² = (x

-

1), the tangent to it at the point whose ordinate is 3 and the x-axis is :

Step-by-Step Verified Solution

y = 3

\Rightarrow

x = 2

Point is (2, 3)

Diff. w.r.t x

2 (y

-

2) y' = 1

\Rightarrow

y^{'} = \frac{1}{2 (y - 2)}

\Rightarrow y_{(2, 3)}^{'} = \frac{1}{2}

\Rightarrow \frac{y - 3}{x - 2} = \frac{1}{2} \Rightarrow x - 2 y + 4 = 0

Area

= \int_{0}^{3} ({(y - 2)}^{2} + 1 - (2 y - 4)) d y

= 9 sq. units