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Question
The equation of the circle circumscribing the triangle formed by pair of tangent and corresponding chord of contact, is
The equation of the circle circumscribing the triangle formed by pair of tangent and corresponding chord of contact, is
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Solution
The correct option is A x2+y2−3x−2y−1=0
The given equation of circle x2+y2−4x−6y−3=0
Comparing it with the generalized circle equation x2+y2+2gx+2fy+c=0, we get g=−2,f=−3,c=−3
Two tangents are drawn from point P (1, -1), which meets the above circle at A and B.
Generalized equation of the circle circumscribing the triangle formed by pair of tangent from point (X1,Y1) and corresponding chord of contact is (x−X1)(x+g)+(y−Y1)(y+f)=0,
Substituting the values of X1,Y1,f,g in the above equation, we get
(x−1)(x−2)+(y+1)(y−3)=0, which simplifies to x2+y2−3x−2y−1=0.
Hence, Option C is correct.
The given equation of circle x2+y2−4x−6y−3=0
Comparing it with the generalized circle equation x2+y2+2gx+2fy+c=0, we get g=−2,f=−3,c=−3
Two tangents are drawn from point P (1, -1), which meets the above circle at A and B.
Generalized equation of the circle circumscribing the triangle formed by pair of tangent from point (X1,Y1) and corresponding chord of contact is (x−X1)(x+g)+(y−Y1)(y+f)=0,
Substituting the values of X1,Y1,f,g in the above equation, we get
(x−1)(x−2)+(y+1)(y−3)=0, which simplifies to x2+y2−3x−2y−1=0.
Hence, Option C is correct.
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