Question

The image of the circle $x^2+y^2-2x=0$ in the line $x+y=2$ is the circle

• A. $x^2+y^2-4x-2y+4=0$
• B. $x^2+y^2+2x=0$
• C. $x^2+y^2-2y=0$
• D. $x^2+y^2-2x-2y+4=0$

Answer 1

The correct option is A $x^2+y^2-4x-2y+4=0$

$x^2+y^2-2x=0$
centre $(1,0)$ radius $=1=r$
So, image of centre $(1,0)$ w.r.t. $(x+y=2)$ is
$\Rightarrow \frac{h-1}{1}=\frac{k-0}{1}=-2\frac{(-1)}{1+1}=1$
$h=2$ and $k=1$
$(2,1)$ is image of $(1,0)$
So, $e{q}^n$ of image circle is
$(x-2{)}^{+}(y-1{)}^2=r^2=1$
$\Rightarrow x^2+y^2-4x-2y+4=0$