坐標幾何

In the figure, $L_1$ and $L_2$ are two straight lines intersecting at a point on the $y$-axis. If the equation of $L_1$ is $x+2y-2=0$, then the equation of $L_2$ is

If $(-2,3)$ is the mid-point of $(a,-1)$ and $(4,b)$, then $b=$

If the straight line $x+y-3=0$ divides the circle $x^2+y^2+2x-ky-4=0$ into two equal parts, then $k=$

The equation of a circle is $x^2+y^2-4x+2y+1=0$. Which of the following is/are true? I. The circle touches the $y$-axis. II. The origin lies outside the circle. III. The centre of the circle lies in the second quadrant.

In the figure, the straight lines $L_1$ and $L_2$ intersect at $(2,4)$. Find the equation of $L_1$.

If the straight line $2x+y+k=0$ passes through the point of intersection of the two straight lines $x+y-3=0$ and $x-y+1=0$, find $k$.

$P(-10,-8)$ and $Q(4,6)$ are two points. If $R$ is a point on the $x$-axis such that $PR=RQ$, then the coordinates of $R$ are

The circle $(x-4)^2+y^2=36$ intersects the positive $x$-axis and positive $y$-axis at $A$ and $B$ respectively. Find $AB$.

If $a<0$ and $b>0$, which of the following may represent the graph of $y=ax+b$ ?

If the length of the line segment joining the points $(2,3)$ and $(k,\ 1-k)$ is $4$, then $k=$