The equation of pair of tangents to the circle ${x^2} + {y^2} - 2x + 4y + 3 = 0$ from $(6, - 5)$, is
$7{x^2} + 23{y^2} + 30xy + 66x + 50y - 73 = 0$
$7{x^2} + 23{y^2} + 30xy - 66x - 50y - 73 = 0$
$7{x^2} + 23{y^2} - 30xy - 66x - 50y + 73 = 0$
None of these
The equations of the tangents to the circle ${x^2} + {y^2} = {a^2}$ parallel to the line $\sqrt 3 x + y + 3 = 0$ are
The number of tangents that can be drawn from $(0, 0)$ to the circle ${x^2} + {y^2} + 2x + 6y - 15 = 0$ is
Consider circle $S$ : $x^2 + y^2 = 1$ and $P(0, -1)$ on it. $A$ ray of light gets reflected from tangent to $S$ at $P$ from the point with abscissa $-3$ and becomes tangent to the circle $S.$ Equation of reflected ray is
The equation of circle with centre $(1, 2)$ and tangent $x + y - 5 = 0$ is
A line $lx + my + n = 0$ meets the circle ${x^2} + {y^2} = {a^2}$ at the points $P$ and $Q$. The tangents drawn at the points $P$ and $Q$ meet at $R$, then the coordinates of $R$ is