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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
65
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C
35
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D
53
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Solution

The correct option is A 103
Given:
Circle touches the x -axis at the point (1,0) and also passes through the point (2,3)

Note:
General equation of circle is given by-
(xh)2+(yr)2=r2

Since the circle passes through (1,0) and (2,3)

We can write the equation of circle as
(12)2+(r3)2=r2

On simplification,

1+r26r+9=r2
16r+9=0
106r=0
6r=10
r=106
r=53
Now diameter is 2r=103

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