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A circle touches Y Axes 2013 and makes an intercept of two unit on the plane xl x axis intercept made made by circle online root 10 x minus 3 Y = 1 is

A circle touches Y Axes 2013 and makes an intercept of two unit on the plane  xl x axis intercept made made by circle online root 10 x minus 3 Y = 1 is
 
 

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Grade:12

1 Answers

Samyak Jain
333 Points
5 years ago
Let r be the radius of given circle.
Distance between y-axis and centre C of the circle is r (\because y-axis is tangent.)
\therefore C \equiv (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.
\therefore by Pythagoras theorem, CP2 = CM2 + PM2
i.e. r2 = 32 + 12 = 10   \Rightarrow  r = \sqrt{10} units
\therefore Centre of the circle is (\sqrt{10} , 3).
Clearly, (\sqrt{10} , 3) satisfies the equation \sqrt{10} x – 3y – 1 = 0,
i.e., given line passes through the centre and is a diameter of the circle.
\therefore intercept made by the circle on the line \sqrt{10} x – 3y – 1 = 0 is equal to
   2r = 2\sqrt{10} units

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