The points $(x_1, y_1), (x_2, y_2), (x_1, y_2),$ and $(x_2, y_1)$ are always:

Suppose $Q$ is a point on the circle with centre $P$ and radius $1$,as shown in the figure. $R$ is a point outside the circle such that $QR = 1$ and $\angle QRP = 2^{\circ}$. Let $S$ be the point where the segment $RP$ intersects the given circle. Then,the measure of $\angle RQS$ equals $......^{\circ}$.

Let $PQ$ and $RS$ be tangents at the extremities of a diameter $PR$ of a circle of radius $r$ such that $PS$ and $RQ$ intersect at a point $X$ on the circumference of the circle,then $2r$ equals

If $x^2+y^2=25$,then $\log _5[\max (3 x+4 y)]$ is

If the inverse point of the point $(3, 2)$ with respect to the circle $x^2+y^2-2x+4y-4=0$ is $(l, m)$,then $(2l+19m) =$

$A$ circle touches both the coordinate axes and the straight line $L \equiv 4x+3y-6=0$ in the first quadrant. If this circle lies below the line $L=0$,then the equation of that circle is