坐標幾何

The equations of two circles are $\begin{cases} x^2+y^2-4x-6y=0 \\ x^2+y^2+4x+6y=0 \end{cases}$. Which of the following is/are true?

I. The two circles have the same centre. II. The two circles have equal radii. III. The two circles pass through the origin.

If the point $(1,1)$, $(3,2)$ and $(7,k)$ are on the same straight line, then $k=$

$A(0,0)$, $B(5,0)$ and $C(2,6)$ are the vertices of a triangle. $P(9,5)$, $Q(6,6)$ and $R(2,-9)$ are three points. Which of the following triangles has/have area(s) greater than the area of $\triangle ABC$? I. $\triangle ABP$ II. $\triangle ABQ$ III. $\triangle ABR$

What is the area of the circle $x^2+y^2-10x+6y-2=0$?

If the two lines $2x-y+1=0$ and $ax+3y-1=0$ do not intersect, then $a=$

If $0<k<h$, which of the following circles intersect(s) the $y$-axis? I. $(x-h)^2+(y-k)^2=k^2$ II. $(x-h)^2+(y-k)^2=h^2$ III. $(x-h)^2+(y-k)^2=h^2+k^2$

If the line $y=mx+3$ divides the circle $x^2+y^2-4x-2y-5=0$ into two equal parts, find $m$.

The mid-points of the sides of a triangle are $(3,4)$, $(2,0)$ and $(4,2)$. Which of the following points is a vertex of the triangle?

The circle $x^2+y^2+4x+ky+4=0$ passes through the point $(1,3)$. The radius of the circle is

Let $A$ and $B$ be the points $(4,-7)$ and $(-6,5)$ respectively. The equation of the line passing through the mid-point of $AB$ and perpendicular to $3x-4y+14=0$ is