坐標幾何

The equation of the perpendicular bisector of the line joining $(1,\ 2)$ and $(7,\ 4)$ is

In the figure, the circle passes through $(0,\ 0)$ and cuts the two axes at $(6,\ 0)$ and $(0,\ -8)$. Its equation is

The equation of a circle is $x^2+y^2-4x-5=0$. Which of the following is/are true?

I. The circle passes through the origin. II. The centre lies on the $x$-axis. III. The line $x-5=0$ touches the circle.

Which of the following systems of inequalities determine the shaded region in the figure?

The point $P$ divides $AB$ internally so that $AP:PB=2:1$. The coordinates of $A$ and $B$ are $(x_1,y_1)$ and $(x_2,y_2)$ respectively. The coordinates of $P$ are

The line $x+y+k=0$ ($k$ being a constant) passes through the centre of the circle $x^2+y^2-2x+4y-6=0$. $k=$

The equation of a circle is $x^2+y^2-2x+5y-7=0$. Which of the following is/are true? I. The circle passes through the point $(-1,1)$. II. The centre of the circle lies in the second quadrant. III. The circle intersects the $x$-axis at two points.

If $a$, $b$ and $c$ are positive real numbers, which of the following graphs could represent the line $ax+by+c=0$?

If the line $2x-3y+c=0$ passes through the point $(1,1)$, then $c=$

The equation of the line passing through $(1,-1)$ and perpendicular to the $x$-axis is