JEE Main 2022 · 25 Jul · Shift 1 · Mathematics Q13

← JEE Main 2022 · 25 Jul · Shift 1

MathematicsSingle correct+4 / -1Question 13 of 90

Let the locus of the centre $(\alpha,\beta)$ , $\beta>0$ , 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 :

\dfrac{32\sqrt2}3

\dfrac{40\sqrt2}3

\dfrac{64}3

\dfrac{32}3

Answer and worked solution

Official answer: C

Locus. $\alpha^2+(\beta-1)^2=(\beta+1)^2$ , i.e. $x^2=4y$ .

Area with $y=4$ : $2\displaystyle\int_0^4\left(4-\frac{x^2}4\right)dx=\frac{64}3$ .

(C)

Topics:Tangents and normals Area between curves

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JEE Main 2022 · 25 Jul · Shift 1, Mathematics question 13