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
B
πsq.units
C
2πsq.units
D
π/2sq.units

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$$= \pi 2^2 - \pi (1)(2)$$$$= 2 \pi$$Mathematics

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