# 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

Samyak Jain
333 Points
4 years ago
Let r be the radius of given circle.
Distance between y-axis and centre C of the circle is r ($\dpi{80} \because$ y-axis is tangent.)
$\dpi{80} \therefore$ C $\dpi{80} \equiv$ (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.
$\dpi{80} \therefore$ by Pythagoras theorem, CP2 = CM2 + PM2
i.e. r2 = 32 + 12 = 10   $\dpi{100} \Rightarrow$  r = $\dpi{80} \sqrt{10}$ units
$\dpi{80} \therefore$ Centre of the circle is ($\dpi{80} \sqrt{10}$ , 3).
Clearly, ($\dpi{80} \sqrt{10}$ , 3) satisfies the equation $\dpi{80} \sqrt{10}$ x – 3y – 1 = 0,
i.e., given line passes through the centre and is a diameter of the circle.
$\dpi{80} \therefore$ intercept made by the circle on the line $\dpi{80} \sqrt{10}$ x – 3y – 1 = 0 is equal to
2r = 2$\dpi{80} \sqrt{10}$ units