Samyak Jain
Last Activity: 5 Years ago
Let r be the radius of given circle.
Distance between y-axis and centre C of the circle is r (
y-axis is tangent.)
C
(r,3).
Draw perpendicular from C on x-axis at say, M.
The perpendicular bisects the intercept made by the circle on the x-axis
because it is a chord of the circle.
Let the circle intersects x-axis at P and Q.
by Pythagoras theorem, CP
2 = CM
2 + PM
2i.e. r
2 = 3
2 + 1
2 = 10
r =
units
Centre of the circle is (
, 3).
Clearly, (
, 3) satisfies the equation
x – 3y – 1 = 0,
i.e., given line passes through the centre and is a diameter of the circle.
intercept made by the circle on the line
x – 3y – 1 = 0 is equal to
2r = 2 units 
