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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
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B
35
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C
65
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D
53
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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.

115072_40347_ans_7bad33633a544a328bd151e48f5e4db6.jpg

Maths

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