坐標幾何

If the polar coordinates of the point $P$ are $(2,150^\circ)$, then the rectangular coordinates of $P$ are

If the straight line $x+3y-211=0$ is perpendicular to the straight line $kx-3y+211=0$, then $k=$

The figure shows the graph of $ax+y=1$ and the graph of $x+by=1$. Which of the following is true?

A circle $C$ touches the $x$-axis and passes through the point $(-3,1)$. If the centre of $C$ lies on the $y$-axis, then the equation of $C$ is

If the polar coordinates of a point are $(6,\ 210^\circ)$, then the rectangular coordinates of the point are

The straight line $2x+7y=5$ is perpendicular to the straight line

In the figure, the two straight lines intersect at a point on the negative $y$-axis. Which of the following must be true? I. $ac>0$ II. $km>0$ III. $am=ck$ IV. $bm=cl$

Let $O$ be the origin. If $A$ and $B$ are points lying on the $x$-axis and the $y$-axis respectively such that the equation of the circumcircle of $\triangle OAB$ is $x^2+y^2-16x-12y=0$, then the equation of the straight line passing through $A$ and $B$ is

A circle cuts the $x$-axis at $P$ and $Q$ such that $PQ=6$. If the coordinates of the centre of the circle are $(-5,2)$, find the equation of the circle.

The coordinates of the points $A$ and $B$ are $(3,9)$ and $(7,1)$ respectively. If $P$ is a point lying on the straight line $y=x+1$ such that $AP=PB$, then the coordinates of $P$ are