# The equation of the circle which touches x-axis and whose centre is (1, 2) is a) x2 +y2 ?2x+4y+1=0 b) x2 +y2 ?2x?4y+1=0 c) x2 +y2 +2x+4y+1=0 d) x2 +y2 +4x+2y+4=0

Solution: When the Circle touches x-axis

Let $(\alpha ,\beta )$ be the centre of the circle , then radius$\\=\left | \beta \right |$

$\therefore$ Equation of the circle is $\\S:(x-\alpha )^2+(y-\beta )^2=\beta ^2$

We have, $C(\alpha ,\beta )=(1,2)$ Hence $r=2$

Now, Equation of a circle is

$\\\Rightarrow (x-1)^2+(y-2)^2=2^2\\ \\\Rightarrow x^2-2x+1+y^2-4y+4=4\\ \\\Rightarrow x^2+y^2-2x-4y+1=0$

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