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

Let $P(3 \cos \alpha, 2 \sin \alpha)$,$\alpha \neq 0$,be a point on the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$,$Q$ be a point on the circle $x^2 + y^2 - 14x - 14y + 82 = 0$,and $R$ be a point on the line $x + y = 5$ such that the centroid of the triangle $PQR$ is $(2 + \cos \alpha, 3 + \frac{2}{3} \sin \alpha)$. Then the sum of the ordinates of all possible points $R$ is:

If the common tangent to the parabolas $y^{2}=4x$ and $x^{2}=4y$ also touches the circle $x^{2}+y^{2}=c^{2}$,then $c$ is equal to

If the image of the point $(-4, 5)$ in the line $x + 2y = 2$ lies on the circle $(x + 4)^2 + (y - 3)^2 = r^2$,then $r$ is equal to:

$A$ circle touches the line $2x + y - 10 = 0$ at $(3, 4)$ and passes through the point $(1, -2)$. Then a point that lies on the circle is