Let the locus of the centre (α, β), β0, 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 :

Question

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 : (A) (32 √2/3) (B) (40 √2/3) (C) (64/3) (D) (32/3)

Tardigrade Admin · Accepted Answer

(α-0)2+(β-1)2=(β+1)2 α2=4 β x2=4 y A=2 ∫ limits04(4-(x2/4)) d x=(64/3)

Q. 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 :

$\frac{32 2}{3}$

$\frac{40 2}{3}$

$\frac{64}{3}$

$\frac{32}{3}$

$(α - 0)^{2} + (β - 1)^{2} = (β + 1)^{2}$
$α^{2} = 4 β$
$x^{2} = 4 y$
$A = 2 0 \int 4 (4 - \frac{x ^{2}}{4}) d x = \frac{64}{3}$

Q. Let the locus of the centre (α,β),β>0, of the circle which touches the circle x2+(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 :

3322​​

3402​​

364​

332​