The length of the diameter of the circle which touches the $x$-axis at the point $(1,0)$ and passes through…
The length of the diameter of the circle which touches the $x$-axis at the point $(1,0)$ and passes through the point $(2,3)$ is
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$\frac{10}{3}$
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$\frac{3}{5}$
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$\frac{6}{5}$
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$\frac{5}{3}$
Solution
Let $(h, k)$ be centre.
$\begin{array}{ll}
(h-1)^2+(k-0)^2=k^2 & \Rightarrow h=1 \\
(h-2)^2+(k-3)^2=k^2 & \Rightarrow k=\frac{5}{3}
\end{array}$
$\therefore$ diameter is $2 \mathrm{k}=\frac{10}{3}$
Asked in: JEE Main 2012 (Offline)
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