The equation of tangent to the circle ${x^2} + {y^2} = {a^2}$ parallel to $y = mx + c$ is
$y = mx \pm \sqrt {1 + {m^2}} $
$y = mx \pm a\sqrt {1 + {m^2}} $
$x = my \pm a\sqrt {1 + {m^2}} $
None of these
At which point on $y$-axis the line $x = 0$ is a tangent to circle ${x^2} + {y^2} - 2x - 6y + 9 = 0$
The centre of the circle passing through the point $(0,1)$ and touching the parabola $y=x^{2}$ at the point $(2,4)$ is
The number of tangents which can be drawn from the point $(-1,2)$ to the circle ${x^2} + {y^2} + 2x - 4y + 4 = 0$ is
$S_1$ and $S_2$ are two concentric circles of radii $1$ and $2$ respectively. Two parallel tangents to $S_1$ cut off an arc from $S_2$. The length of the arc is
If the tangent at a point $P(x,y)$ of a curve is perpendicular to the line that joins origin with the point $P$, then the curve is