From the origin chords are drawn to the circle ${(x - 1)^2} + {y^2} = 1$. The equation of the locus of the middle points of these chords is
${x^2} + {y^2} - 3x = 0$
${x^2} + {y^2} - 3y = 0$
${x^2} + {y^2} - x = 0$
${x^2} + {y^2} - y = 0$
If the line $3x + 4y - 1 = 0$ touches the circle ${(x - 1)^2} + {(y - 2)^2} = {r^2}$, then the value of $r$ will be
The equations of tangents to the circle ${x^2} + {y^2} - 22x - 4y + 25 = 0$ which are perpendicular to the line $5x + 12y + 8 = 0$ are
The equation of the normal at the point $(4,-1)$ of the circle $x^2+y^2-40 x+10 y=153$ is
The line $y = mx + c$ will be a normal to the circle with radius $r$ and centre at $(a, b)$, if
Two tangents drawn from the origin to the circle ${x^2} + {y^2} + 2gx + 2fy + c = 0$ will be perpendicular to each other, if