Question

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

• A. $4\pi sq.units$
• B. $\pi sq.units$
• C. $2\pi sq.units$
• D. $\pi /2sq.units$

Answer 1

Answer: (C)

$2\pi sq.units$

Circle
$x^2-2x+y^2-4y+1=0$
$(x-1{)}^2+(y-2{)}^2=4$
Ellipse
$x^2-2x+4y^2-16y+13=0$
$(x-1{)}^2+4(y-2{)}^2=4$
From the figure,
The required answer $=$ Area of circle $-$ Area of ellipse
$=\pi 2^2-\pi \left(1\right)\left(2\right)$
$=2\pi$