Circle

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

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

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)

If a tangent to the circle \(x^2+y^2=1\) intersect the co-ordinate axes at distinct points \(P\) and \(Q\), then the locus of the mid-point of \(P Q\) is

A normal is drawn at the point \(P\) to the circle \(x^2+y^2=25\), which is inclined at \(45^{\circ}\) with the straight line \(y=6\). Then, the point lies on the straight line

If the straight line \(y=m x+c\), touches the circle \(x^2+y^2=a^2\) at a point, then \(c^2\) is

The locus of the mid-point of the chord if contact of tangents drawn from points lying on the straight line \(4x - 5y = 20\) to the circle \({x^2} + {y^2} = 9\) is

Equation of circle which passes through the points (1, \(-\)2) and (3, \(-\)4) and touch the X-axis is