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Question

A circle passes through the points (2,3) and (4,5). If its centre lies on the line, y4x+3=0, then its radius is equal to :

A
2
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B
5
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C
2
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D
1
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Solution

The correct option is A 2

Let the coordinates of centre whichlies on the line y=4x3, be
: O(a,4a3)
Using distance formula
(a2)2+(4a6)2=(a4)2+(4a8)2(a2)2(a4)2=(4a8)2(4a6)22(2a6)=2(8a14)2a6=8a+14a=2

Hence the radius of the circle
=(a2)2+(4a6)2=0+22=2

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