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
The lines $y - y_1 = m (x - x_1) \pm a \,\sqrt {1\,\, + \,\,{m^2}} $ are tangents to the same circle . The radius of the circle is :
If the line $lx + my = 1$ be a tangent to the circle ${x^2} + {y^2} = {a^2}$, then the locus of the point $(l, m)$ is
Let $O$ be the centre of the circle $x ^2+ y ^2= r ^2$, where $r >\frac{\sqrt{5}}{2}$. Suppose $P Q$ is a chord of this circle and the equation of the line passing through $P$ and $Q$ is $2 x+4 y=5$. If the centre of the circumcircle of the triangle $O P Q$ lies on the line $x+2 y=4$, then the value of $r$ is. . . .
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 $2x - 4y = 9$ and $6x - 12y + 7 = 0$ are the tangents of same circle, then its radius will be