坐標幾何

The line $y=mx+c$ is perpendicular to the line $y=3-2x$. Find $m$.

In the figure, $A(5,3)$, $B(b,1)$ and $C(c,1)$ are the vertices of a triangle. If $AB=AC$, then $b+c=$

In the figure, which region represents the solution to the following inequalities? $\begin{cases}x-3y\le 0\\x-y+2\ge 0\\x+y-4\ge 0\end{cases}$

Which of the following straight lines divide(s) the circle $(x-1)^2+(y+1)^2=1$ into two equal parts? I. $x-y-2=0$ II. $x+y+2=0$ III. $x-y+2=0$

The equation of a circle is $x^2+y^2-4x+2y+1=0$. Which of the following is/are true? I. The centre is $(-2,1)$. II. The radius is 2 units. III. The circle intersects the $y$-axis at two distinct points.

Two perpendicular lines $kx+y-4=0$ and $x-2y+3=0$ intersect at the point $(h,k)$. Find $h$ and $k$.

Which of the following represents a circle?

In the figure, $L_1$ and $L_2$ are two straight lines perpendicular to each other and intersecting at $P$ on the $y$-axis. If the equation of $L_1$ is $y=ax-5$, then the equation of $L_2$ is

Let $p=2x+3y$. Under the following constraints $x\ge0$ $y\ge0$ $x\le4$ $y\le3$ $x+y\le6$ what is the greatest value of $p$?

The distance between $(1-k,\ k)$ and $(2,\ 1+k)$ is $\sqrt{26}$, $k=$