Q. 113.5( 10 Votes )

Find the equation of the circle concentric with the circle x2 + y2 – 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:


x2 + y2 + 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


x2 + 4 – 4x + y2 + 9 – 6y = 4


x2 + y2 – 4x – 6y + 9 = 0


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