If the line $y = \sqrt{3}x + k$ touches the circle $x^2 + y^2 = 16$,then $k =$

The equation of the pair of tangents drawn from the point $(1, 1)$ to the circle $x^2 + y^2 + 2x + 2y + 1 = 0$ is:

If the line $(x + g) \cos \theta + (y + f) \sin \theta = k$ is tangent to the circle $x^2 + y^2 + 2gx + 2fy + c = 0$,then:

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?

If $\theta$ is the acute angle between the curves $x^2+y^2=4$ and $y^2=3x$, then $\tan \theta=$

The line $y = mx + c$ will be a normal to the circle with radius $r$ and centre at $(a, b)$,if