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Question

If one of the diameters of the circle, given by the equation x2+y24x+6y12=0, is a chord of a circle S, whose centre is at (-3,2), then the radius of S is

A
52
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B
53
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C
5
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D
10
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Solution

The correct option is B 53
Given equation of a circle is x2+y24x+6y12=0
Whose centre is (2, -3) and radius
=22+(3)2+12=4+9+12=5



Now, according to given information, we have the following figure.
x2+y24x+6y12=0
Clearly, AOBC ad O is mid-point of the chord.
Now, in ΔAOB, we have
OA=(32)2+(2+3)2=25+25=50=52
And OB=5
AB=OA2+OB2=50+25=75=53


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