Q. 113.5( 10 Votes )

# Find the equation of the circle concentric with the circle x^{2} + y^{2} – 4x – 6y – 3 = 0 and which touches the y-axis.

Answer :

The given image of the circle is:

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

x^{2} + y^{2} + 2gx + 2fy + c = 0

Also,

Radius r =

Now,

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}

x^{2} + 4 – 4x + y^{2} + 9 – 6y = 4

x^{2} + y^{2} – 4x – 6y + 9 = 0

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