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Question

Tangents drawn, from the point P(1,8) to the circle $$x^{2} + y^{2} - 6x - 4y -11= 0$$ touch the circle at the points A and B. The equation of the circumcircle of the triangle PAB is


A
x2+y2+4x6y+19=0
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B
x2+y24x10y+19=0
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C
x2+y22x+6y29=0
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D
x2+y26x4y+19=0
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Solution

The correct option is B $$x^{2} + y^{2} - 4x - 10y +19 = 0$$
Note: Circumcircle of triangle $$PAB$$ will always pass through the centre of the circle on which $$A$$ and $$B$$ are lying i.e. the circle to which tangents are drawn from $$P$$.
Note: Also $$PO$$ acts as the diameter of the circumcircle.
$$\therefore $$ Equation of the circumcircle:
$$\Rightarrow (x-1)(x-3)+(y-8)(y-2)=0$$
$$\Rightarrow x^{2}-3x-x+3+y^{2}-2y-8y+16=0$$
$$\Rightarrow x^{2}+y^{2}-4x-10y+19=0$$
$$\therefore B)$$ Answer.

1060351_1007134_ans_5cbeb4a85e3d4e8d962ea1902b33d1a0.png

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