Question

The equation of the image of the circle $(x-3{)}^2+(y-2{)}^2=1$ by the mirror x + y = 19 is

• A. $(x-14{)}^2+(y-13{)}^2=1$
• B. $(x-15{)}^2+(y-14{)}^2=1$
• C. $(x-16{)}^2+(y-15{)}^2=1$
• D. $(x-17{)}^2+(y-16{)}^2=1$

Answer 1

The correct option is D $(x-17{)}^2+(y-16{)}^2=1$

The image of the circle has same radius but center different. If center of image circle is $(\alpha ,\beta )$, then
$\frac{\alpha -3}{1}=\frac{\beta -2}{1}=-\frac{2(3+2-19)}{1^2+1^2}\Rightarrow \alpha -3=\beta -2=14\Rightarrow \alpha =17,\beta =16$
$\therefore$ Required circle is $(x-17{)}^2+(y-16{)}^2=1$