Point $M$ moved along the circle $(x - 4)^2 + (y - 8)^2 = 20 $. Then it broke away from it and moving along a tangent to the circle, cuts the $x-$ axis at the point $(- 2, 0)$ . The co-ordinates of the point on the circle at which the moving point broke away can be :
$\left( { - \,\frac{3}{5}\,\,,\,\,\frac{{46}}{5}} \right)$
$\left( { - \,\frac{2}{5}\,\,,\,\,\frac{{44}}{5}} \right)$
$(6, 4)$
$(B)$ or $(C)$ both
The equation of the normal to the circle ${x^2} + {y^2} - 2x = 0$ parallel to the line $x + 2y = 3$ is
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
If the centre of a circle is $(2, 3)$ and a tangent is $x + y = 1$, then the equation of this circle is
The length of tangent from the point $(5, 1)$ to the circle ${x^2} + {y^2} + 6x - 4y - 3 = 0$, is
The equation of the circle whose radius is $5$ and which touches the circle ${x^2} + {y^2} - 2x - 4y - 20 = 0$ externally at the point $(5, 5)$ is