The equation of a line parallel to the line $3x + 4y = 0$ and touching the circle $x^{2} + y^{2} = 9$ in the first quadrant is:

The angle between the tangents drawn from the origin to the circle $(x - 7)^2 + (y + 1)^2 = 25$ is:

Let $A$ be the center of the circle $x^2 + y^2 - 2x - 4y - 20 = 0$. If $B(1, 7)$ and $D(4, -2)$ are points on the circle,and the tangents at $B$ and $D$ meet at $C$,then the area of the quadrilateral $ABCD$ is:

$O(0,0)$ and $A(1,0)$ are the centers of two unit circles $C_1$ and $C_2$ respectively. $C_3$ is also a unit circle having its center above the $X$-axis and passing through $O$ and $A$. The equation of the common tangent to $C_1$ and $C_3$ which does not intersect the circle $C_2$ is

Suppose two tangents $PA$ and $PB$ are drawn to the circle centered at $C(1, 2)$ from the point $P(16, 7)$. If the area of the quadrilateral $PACB$ is $75$ square units,then the radius of the circle is:

The equation of the tangent to the circle $x^2+y^2-9=0$ making an angle $60^{\circ}$ with the $X$-axis is