If the tangents are drawn to the circle x2+y2=12 at the point where it meets the circle x2+y2−5x+3y−2=0, then the point of intersection of these tangents is
A
(6,−185)
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B
(−6,185)
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C
(7,−186)
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D
(8,−185)
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Solution
The correct option is A(6,−185)
Let (h,k) be the point of intersection of the tangents.
Then the chord of contact of tangents is the common chord of the circle x2+y2=12 and x2+y2−5x+3y−2=0.
i.e., S1−S2=0 ⇒5x−3y−10=0
Also, the equation of the chord of contact w.r.t. P is T=0
i.e., hx+ky−12=0
Equations hx+ky−12=0 and 5x−3y−10=0 represent the same line. ∴h5=k−3=−12−10 ⇒h=6,k=−185
Hence, the required point is (6,−185).