Question

# 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:

A
103
B
35
C
65
D
53

Solution

## The correct option is A $$\dfrac {10} 3$$Let $$(h,k)$$ be the centre .$$(h-1)^2 +(k-0)^2=k^2 \Rightarrow h=1$$$$\displaystyle (h-2)^2 +(k-3)^2=k^2 \Rightarrow k=\frac{5}{3}$$$$\therefore$$ diameter is $$\displaystyle 2k=\frac{10}{3}$$Hence, option 'A' is correct.Maths

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