坐標幾何

If the rectangular coordinates of the point $A$ are $(-1,1)$, then the polar coordinates of $A$ are

Find the equation of the straight line which is perpendicular to the straight line $x+2y+3=0$ and passes through the point $(1,3)$.

The figure shows the graph of the straight line $ax+by+1=0$. Which of the following is true?

A circle $C$ touches the $y$-axis. If the coordinates of the centre of $C$ are $(-3,4)$, then the equation of $C$ is

Let $a$ be a constant. If the circle $x^2+y^2+ax-6y-3=0$ passes through the point $(-2,3)$, then the area of the circle is

If the polar coordinates of the points $A$ and $B$ are $(5,45^\circ)$ and $(12,135^\circ)$ respectively, then the distance between $A$ and $B$ is

If $k<0$, which of the following may represent the graph of the straight line $x-y=k$ ?

The straight line $4x+y-2=0$ is perpendicular to the straight line

If the straight line $5x-3y=30$ cuts the $x$-axis and the $y$-axis at $A$ and $B$ respectively, then the coordinates of the mid-point of $AB$ are

If the points $(0,0)$, $(2,0)$ and $(1,b)$ are the vertices of an equilateral triangle, then $b=$