QJEEM22Ma23fb: JEE Main 2022 Mathematics - Class 12 JEEM22Ma23fb Solution: Let the locus of the centre ( α , β ) , β > 0 , of the circle…

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QJEEM22Ma23fb: JEE Main 2022 Mathematics - Class 12 JEEM22Ma23fb Solution: Let the locus of the centre ( α , β ) , β > 0 , of the circle…

Let the locus of the centre $(α, β), β > 0$ , of the circle which touches the circle $x^{2} + (y - 1)^{2} = 1$ externally and also touches the $x$ -axis be $L$ . Then the area bounded by $L$ and the line $y = 4$ is:

Multiple Choice Options

A 3223
B 4023
C 643
D 323

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Accepted Answer

JEE Main 2022 (Online) 25th July Morning Shift Mathematics - Area Under The Curves Question 67 English Explanation 1

Radius of circle

S

touching

x

-axis and centre

(\alpha, \beta)

is

|\beta|

. According to given conditions

\begin{aligned} α^{2} + (β - 1)^{2} = (| β | + 1)^{2} \\ α^{2} + β^{2} - 2 β + 1 = β^{2} + 1 + 2 | β | \\ α^{2} = 4 β as β > 0 \end{aligned}

\therefore \quad

Required louse is

L: x^{2}=4 y

JEE Main 2022 (Online) 25th July Morning Shift Mathematics - Area Under The Curves Question 67 English Explanation 2

The area of shaded region

=2 \int_{0}^{4} 2 \sqrt{y} d y

\begin{aligned} = 4 . {[\frac{y^{\frac{3}{2}}}{\frac{3}{2}}]}_{0}^{4} \\ = \frac{64}{3} square units. \end{aligned}

QJEEM22Ma23fb: JEE Main 2022 Mathematics - Class 12 JEEM22Ma23fb Solution: Let the locus of the centre ( α , β ) , β > 0 , of the circle…

Multiple Choice Options

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