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