The locus of the middle points of chords of the circle $x^2+y^2=25$ which are parallel to the line $x-2 y+3=0$ is

What is the set of values of a for which the point ( $2 a, a+1$ ) is an interior point of the larger segment of the circle $x^2+y^2-2 x-2 y-8=0$ made by the chord $x-y+1=0$.

The locus of the point of intersection of the lines $ x=a\left(\frac{1-t^{2}}{1+t^{2}}\right) $ and $ y=\frac{2 a t}{1+t^{2}} $ represent $ (t $ being a parameter)

The locus of the mid-point of a chord of the circle $ x^{2}+y^{2}=4 $, which subtends a right angle at the origin is