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

If the equation of the common tangent at the point $(1, -1)$ to the two circles,each of radius $13$,is $12x + 5y - 7 = 0$,then the centers of the two circles are

The equation of the circle passing through the point $(-1, -3)$ and touching the line $4x + 3y - 12 = 0$ at the point $(3, 0)$ is

If the line $x = 7$ touches the circle ${x^2} + {y^2} - 4x - 6y - 12 = 0$,then the coordinates of the point of contact are:

The angle between the tangents drawn from the origin to the circle $x^2+y^2+4x-6y+4=0$ is

The tangent to the parabola $y = x^2 + 6$ at the point $P(1, 7)$ touches the circle $x^2 + y^2 + 16x + 12y + c = 0$ at point $Q$. What are the coordinates of $Q$?