Equation of the pair of tangents drawn from the origin to the circle ${x^2} + {y^2} + 2gx + 2fy + c = 0$ is
$gx + fy + c({x^2} + {y^2})$
${(gx + fy)^2} = {x^2} + {y^2}$
${(gx + fy)^2} = {c^2}({x^2} + {y^2})$
${(gx + fy)^2} = c({x^2} + {y^2})$
If the length of the tangents drawn from the point $(1,2)$ to the circles ${x^2} + {y^2} + x + y - 4 = 0$ and $3{x^2} + 3{y^2} - x - y + k = 0$ be in the ratio $4 : 3$, then $k =$
Square of the length of the tangent drawn from the point $(\alpha ,\beta )$ to the circle $a{x^2} + a{y^2} = {r^2}$ is
The equation of the tangent to the circle ${x^2} + {y^2} - 2x - 4y - 4 = 0$ which is perpendicular to $3x - 4y - 1 = 0$, 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
The normal to the circle ${x^2} + {y^2} - 3x - 6y - 10 = 0$at the point $(-3, 4)$, is