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Find the equation of the circle concentric with the circle x2 + y2 – 4x – 6y – 3 = 0 and which touches the y-axis.

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The given image of the circle is:

We know that the general equation of the circle is given by: 

x2 + y2 + 2gx + 2fy + c = 0 

Also, 

Radius r =

r = \(\sqrt{g^2+f^2-c}\) 

Now,

 r = \(\sqrt{(2)^2+(3)^2-(-3)}\) 

r = \(\sqrt{4+9+3}\)

r = 4 units. 

We need to the find the equation of the circle which is concentric to the given circle and touches y-axis. 

The centre of the circle remains the same. 

Now, y-axis will be tangent to the circle. 

Point of contact will be (0, 3) 

Therefore, radius = 2 

Now, 

Equation of the circle: 

(x – 2)2 + (y – 3)2 = (2)2

x2 + 4 – 4x + y2 + 9 – 6y = 4

= x2 + y2 – 4x – 6y + 9 = 0

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