The coordinates of the point on the circle $x^2 + y^2 - 12x - 4y + 30 = 0$ which is farthest from the origin are:

If $(x, y)$ is a variable point on the curve $x^2 + y^2 - 2x - 2y - 2 = 0$,then the minimum value of the expression $\frac{8}{(x - 1)^2} - \frac{(y - 1)^2}{4}$ is equal to

The common chord of two intersecting circles $c_1$ and $c_2$ subtends angles of $90^\circ$ and $60^\circ$ at their respective centres. If the distance between their centres is $\sqrt{3} + 1$,then the radii of $c_1$ and $c_2$ are:

Tangents are drawn from the point $(17, 7)$ to the circle $x^2 + y^2 = 169$.
Statement-$1$: These tangents are perpendicular to each other.
Statement-$2$: From every point on the circle $x^2 + y^2 = 338$,perpendicular tangents can be drawn to the given circle.

The centre$(s)$ of the circle$(s)$ passing through the points $(0, 0)$ and $(1, 0)$ and touching the circle $x^2 + y^2 = 9$ is/are:

If $\theta$ is the angle subtended at $P(x_1, y_1)$ by the circle $S \equiv x^2 + y^2 + 2gx + 2fy + c = 0$,then