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

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If the length of the tangents from (a,b) to the circles x2+y2−4x−5=0 and x2+y2+6x−2y+6=0 are equal then 10a−2b is equal to

The correct option is B −11Radical axis of given circle is S1−S2=0 ⇒10x−2y+11=0 (a,b) lies on Radical axis ∵ Length of tangents frawn from any point on radical axis to circles are equal ∴10a−2b=−11

If the length of the tangents from $(a, b)$ to the circles $x^{2} + y^{2} - 4 x - 5 = 0$ and $x^{2} + y^{2} + 6 x - 2 y + 6 = 0$ are equal then $10 a - 2 b$ is equal to

The correct option is B $- 11$
Radical axis of given circle is $S_{1} - S_{2} = 0$
$\Rightarrow 10 x - 2 y + 11 = 0$
$(a, b)$ lies on Radical axis $∵$ Length of tangents frawn from any point on radical axis to circles are equal
$∴ 10 a - 2 b = - 11$