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  • 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

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

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Solution: When the Circle touches x-axis

Let (alpha ,eta ) be the centre of the circle , then radius\=left | eta ight |

herefore Equation of the circle is \S:(x-alpha )^2+(y-eta )^2=eta ^2

We have, C(alpha ,eta )=(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

Posted by

Deependra Verma

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