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
B
x2+y24x10y+19=0
C
x2+y22x+6y29=0
D
x2+y26x4y+19=0

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.Maths

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