If O is the origin and OP, OQ are the tangents from the origin to the circle x2+y2ā6x+4y+8=0, the circumcenter of the triangle OPQ is
A
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B
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C
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D
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Solution
The correct option is B Now PQ is the chord of contact of the tangents from the origin to the circle x2+y2−6x+4y+8=0→(1) Equation of PQ is3x−2y−8=0→(2) Equation of a circle passing through the intersection of (1) and (2) is x2+y2−6x+4y+8+λ(3x−2y−8)=0→(3) if this represents the circumcircle of the triangle OAB, it passes through O(0, 0), so λ=1and the equation (3) becomesx2+y2−3x+2y=0 ∴ The required coordinates of the centre are(32,−1)