The line $lx + my + n = 0$ is normal to the circle $x^2 + y^2 + 2gx + 2fy + c = 0$,if

If $\theta$ is the angle between the pair of tangents drawn from a point $P(x_1, y_1)$ to the circle $S = x^2 + y^2 + 2gx + 2fy + c = 0$,then which of the following is true?

The equation of the tangent to the circle at the point $(1, -1)$,whose center is the point of intersection of the straight lines $x - y = 1$ and $2x + y = 3$,is:

If $y=\sqrt{3}x+k_1$ and $y=\sqrt{3}x+k_2$ are two parallel tangents of a circle of radius $2 \text{ units}$,then $|k_1-k_2|$ is equal to

If $2x - 3y + 5 = 0$ and $4x - 5y + 7 = 0$ are the equations of the normals drawn to a circle and $(2, 5)$ is a point on the given circle,then the radius of the circle is

If the tangent and the normal at the point $(\sqrt{3}, 1)$ to the circle $x^2+y^2=4$,and the $X$-axis form a triangle,then the area (in sq. units) of this triangle is