Length of the tangent drawn from any point on the circle ${x^2} + {y^2} + 2gx + 2fy + {c_1} = 0$ to the circle ${x^2} + {y^2} + 2gx + 2fy + c = 0$ is
$\sqrt {{c_1} - c} $
$\sqrt {c - {c_1}} $
$\sqrt {{c_1} + c} $
None of these
The line $2 x - y +1=0$ is a tangent to the circle at the point $(2,5)$ and the centre of the circle lies on $x-2 y=4$. Then, the radius of the circle is
Given the circles ${x^2} + {y^2} - 4x - 5 = 0$and ${x^2} + {y^2} + 6x - 2y + 6 = 0$. Let $P$ be a point $(\alpha ,\beta )$such that the tangents from P to both the circles are equal, then
Tangents drawn from origin to the circle ${x^2} + {y^2} - 2ax - 2by + {b^2} = 0$ are perpendicular to each other, if
A circle touches the $y$ -axis at the point $(0,4)$ and passes through the point $(2,0) .$ Which of the following lines is not a tangent to this circle?
If the tangent at $\left( {1,7} \right)$ to the curve ${x^2} = y - 6$ touches the circle ${x^2} + {y^2} + 16x + 12y + c = 0$ then the value of $c$ is: