If the centre of a circle is $(2, 3)$ and a tangent is $x + y = 1$, then the equation of this circle is
${(x - 2)^2} + {(y - 3)^2} = 8$
${(x - 2)^2} + {(y - 3)^2} = 3$
${(x + 2)^2} + {(y + 3)^2} = 2\sqrt 2 $
${(x - 2)^2} + {(y - 3)^2} = 2\sqrt 2 $
A circle is drawn with $y- $ axis as a tangent and its centre at the point which is the reflection of $(3, 4)$ in the line $y = x$. The equation of the circle is
If the ratio of the lengths of tangents drawn from the point $(f,g)$ to the given circle ${x^2} + {y^2} = 6$ and ${x^2} + {y^2} + 3x + 3y = 0$ be $2 : 1$, then
Number of integral points interior to the circle $x^2 + y^2 = 10$ from which exactly one real tangent can be drawn to the curve $\sqrt {{{\left( {x + 5\sqrt 2 } \right)}^2} + {y^2}} \, - \sqrt {{{\left( {x - 5\sqrt 2 } \right)}^2} + {y^2}\,} \, = 10$ are (where integral point $(x, y)$ means $x, y \in I)$
The length of tangent from the point $(5, 1)$ to the circle ${x^2} + {y^2} + 6x - 4y - 3 = 0$, is
The angle between the tangents drawn from the origin to the circle $(x -7)^2 + (y + 1)^2 = 25$ is :-