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

If a circle,whose centre is $(-1, 1)$,touches the straight line $x + 2y + 12 = 0$,then the coordinates of the point of contact are

Find the equation of the normal to the circle $x^2 + y^2 - 5x + 2y - 48 = 0$ at the point $(5, 6)$.

The tangent to the parabola $y = x^2 + 6$ at the point $(1, 7)$ touches the circle $x^2 + y^2 + 16x + 12y + c = 0$ at which point?

Consider the following statements:
Assertion $(A)$: The circle $x^2 + y^2 = 1$ has exactly two tangents parallel to the $x$-axis.
Reason $(R)$: $\frac{dy}{dx} = 0$ on the circle exactly at the points $(0, \pm 1)$.
Of these statements:

The angle between the tangents drawn from the point $(2, 2)$ to the circle $x^2 + y^2 + 4x + 4y + c = 0$ is $\cos^{-1}\left(\frac{7}{16}\right)$. If two such circles exist,then the sum of the values of $c$ is: