Question

The equation of the circle in the first quadrant touching each coordinate axis at a distance of one unit from the origin is
a) x2 +y2 −2x−2y+1=0
b) x2 +y2 −2x−2y−1=0

Answer 1

$\text{From the given information it is clear that,}$

$\text{Centre of the circle (h,k)=(1,1)}$

$\text{Radius of the circle, r= 1 unit}$

$\text{The equation of the circle is}$

$\bf(x-h)^2+(y-k)^2=r^2$

$(x-1)^2+(y-1)^2=1^2$

$x^2-2x+1+y^2-2y+1=1$

$\bf\;x^2+y^2-2x-2y+1=0$

$\therefore\textbf{The equation of the required circle is}$

$\bf\;x^2+y^2-2x-2y+1=0$

$\implies\textbf{Option (a) is correct}$

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