Obtaining Centre and Radius of a Circle from General Equation of a Circle
If one of the...
Question
If one of the diameters of the circle, given by the equation x2+y2−4x+6y−12=0, is a chord of a circle S, whose centre is at (-3,2), then the radius of S is
A
5√2
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B
5√3
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C
5
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D
10
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Solution
The correct option is B5√3 Given equation of a circle is x2+y2−4x+6y−12=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+y2−4x+6y−12=0 Clearly, AO⊥BC ad O is mid-point of the chord. Now, in ΔAOB, we have OA=√(−3−2)2+(2+3)2=√25+25=√50=5√2 And OB=5 ∴AB=√OA2+OB2=√50+25=√75=5√3