Coordinate Geometry Questions

Consider a family of circles which are passing through the point $(-1,1)$ and are tangent to the $x$ -axis. If $(h,k)$ are the coordinates of the centre of the circles, then the set of values of $k$ is given by the interval:

The normal to a curve at $P(x,y)$ meets the $x$ -axis at $G$. If the distance of $G$ from the origin is twice the abscissa of $P$, then the curve is a:

Let $A(h,k)$, $B(1,1)$ and $C(2,1)$ be the vertices of a right angled triangle with $AC$ as its hypotenuse. If the area of the triangle is $1$, then the set of values which $k$ can take is given by:

Let $P=(-1,0)$, $Q=(0,0)$ and $R=(3,3\sqrt{3})$ be three points. The equation of the bisector of the angle $PQR$ is:

If one of the lines of $m{y}^2+(1-m^2)xy-m{x}^2=0$ is a bisector of the angle between the lines $xy=0$, then $m$ is: