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.
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
Radius r =
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
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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