The line $3x - 4y = 0$ is:

The point at which the normal to the circle $x^2 + y^2 + 4x + 6y - 39 = 0$ at the point $(2, 3)$ meets the circle again is:

If the tangent at a point $P$ on the circle $x^2 + y^2 + 6x + 6y = 2$ meets the line $5x - 2y + 6 = 0$ at a point $Q$ on the $y$-axis,then the length of $PQ$ is . . . . .

Abscissae of points on the curve $xy = (c + x)^2$,the normal at which cuts off numerically equal intercepts from the axes of coordinates is/are:

The area of the triangle formed by the positive $x$-axis and the normal and the tangent to the circle $x^2 + y^2 = 4$ at $(1, \sqrt{3})$ 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