Tangents drawn from origin to the circle ${x^2} + {y^2} - 2ax - 2by + {b^2} = 0$ are perpendicular to each other, if
$a - b = 1$
$a + b = 1$
${a^2} = {b^2}$
${a^2} + {b^2} = 1$
If $a > 2b > 0$ then the positive value of m for which $y = mx - b\sqrt {1 + {m^2}} $ is a common tangent to ${x^2} + {y^2} = {b^2}$ and ${(x - a)^2} + {y^2} = {b^2}$, is
The line $y = mx + c$ will be a normal to the circle with radius $r$ and centre at $(a, b)$, if
If the straight line $ax + by = 2;a,b \ne 0$ touches the circle ${x^2} + {y^2} - 2x = 3$ and is normal to the circle ${x^2} + {y^2} - 4y = 6$, then the values of a and b are respectively
The line $2x - y + 1 = 0$ is tangent to the circle at the point $(2, 5)$ and the centre of the circles lies on $x-2y=4$. The radius of the circle is
If the centre of a circle is $(2, 3)$ and a tangent is $x + y = 1$, then the equation of this circle is