Chord with Midpoint

Let the circle $x^2+y^2=16$ and line passing through $\left(1,2\right)$ cuts the circle at $A$ and $B$ then the locus of the midpoint of $AB$ is:

Find the equation of the chord of the circle $x^2+y^2-8x+2y+1=0$, whose middle point is $\left(5, 2\right)$.

The locus of the mid points of the chords of the circle $x^2+y^2-2bx=0$ passing through the origin 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

STATEMENT-1: The locus of midpoint of chords of circle $x^2+y^2=4$ which subtends an angle of $\frac{\pi }{2}$ at centre of the circle is $x^2+y^2=1$.
STATEMENT-2: The locus of midpoint of chords of circle $x^2+y^2=r^2$ subtending an angle $\theta$ at centre of the circle is  $x^2+y^2=r^2{\cos }^2\left(\frac{\theta }{2}\right)$.

Find the equation of chord having midpoint as (2, -1) to the circle ${\text{x}}^2+{\text{y}}^2-4\text{x}-2\text{y}-10=0$

The distance between the chords of contact of tangents to the circle, $x^2+y^2+2gx+2fy+c=0$ from the origin and the point $\left(g,f\right)$ is:

Equation of the circle, whose diameter is the chord $x+y=1$ of the circles $x^2+y^2=4$ , is -

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

The locus of the midpoints of the chords of the circle $x^2+y^2=16$ which are tangents to the hyperbola $9x^2-16y^2=144$ is

The equation of the chord of the circle $x^2+y^2=81$, which is bisected at the point $\left(-2, 3\right)$, is

The equation of the chord of the circle $x^2+y^2=81$, which is bisected at the point $(-2, 3)$, is:

The equation of the chord of the circle $x^2+y^2=81$, which is bisected at the point $(-2,3)$, is

A variable chord is drawn through the origin to the circle $x^2+y^2-2ax=0$. The locus of the centre of the circle drawn on this chord as diameter is

The equation of the chord of the circle, $x^2+y^2=a^2$ having $\left(x_1, y_1\right)$ as its mid point, is

The equation of the chord of the circle $x^2+y^2=81$, which is bisected at the point $\left(-2, 3\right)$, is

The equation of the chord of the circle $x^2+y^2=81$, which is bisected at the point $(-2, 3)$, is

The equation of the chord of the circle $x^2+y^2=81$, which is bisected at the point $(-2, 3)$, is