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Question

Find the equation of the circle concentric with
x2+y24x6y3=0
and which touches the y-axis.

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Solution

The given equation of circle is
x2+y24x6y3=0 (i)
centre is (g,f)=(2,3)
The required circle is concentric with (i)
so, they have same centre = (2, 3)
Also, the required circle touches y - axis at A
CA = radius = 2
equation of circle is
(x2)2+(y3)2=4
x2+y24x6y+9=0


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