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Question

Find the area inside the circle $$\displaystyle x^{2}-2x+y^{2}-4y+1=0$$ and outside the ellipse $$\displaystyle x^{2}-2x+4y^{2}-16y+13=0$$:


A
4πsq.units
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B
πsq.units
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C
2πsq.units
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D
π/2sq.units
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Solution

The correct option is A $$\displaystyle 2\pi sq.units$$
Circle
$$\displaystyle x^{2}-2x+y^{2}-4y+1=0$$
$$\displaystyle (x-1)^{2}+(y-2)^{2}=4$$ 
Ellipse
 $$\displaystyle x^{2}-2x+4y^{2}-16y+13=0$$
 $$\displaystyle (x-1)^{2}+4(y-2)^{2}=4$$
From the figure,
The required answer $$=$$ Area of circle $$-$$ Area of ellipse
$$ =  \pi 2^2 -  \pi (1)(2)$$
$$ =  2 \pi$$
350540_260720_ans.png

Mathematics

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