If a line passing through origin touches the circle ${(x - 4)^2} + {(y + 5)^2} = 25$, then its slope should be
$ \pm \frac{3}{4}$
$0$
$ \pm \,3$
$ \pm \,1$
A tangent drawn from the point $(4, 0)$ to the circle $x^2 + y^2 = 8$ touches it at a point $A$ in the first quadrant. The co-ordinates of another point $B$ on the circle such that $l\, (AB) = 4$ are :
The equation of the normal to the circle ${x^2} + {y^2} = 9$ at the point $\left( {\frac{1}{{\sqrt 2 }},\frac{1}{{\sqrt 2 }}} \right)$ is
If the centre of a circle is $(-6, 8)$ and it passes through the origin, then equation to its tangent at the origin, is
The equation of pair of tangents to the circle ${x^2} + {y^2} - 2x + 4y + 3 = 0$ from $(6, - 5)$, 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