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
${x^2} + {y^2} - 3x = 0$
${x^2} + {y^2} - 3y = 0$
${x^2} + {y^2} - x = 0$
${x^2} + {y^2} - y = 0$
The equation of the tangent to the circle ${x^2} + {y^2} = {r^2}$ at $(a,b)$ is $ax + by - \lambda = 0$, where $\lambda $ is
Tangents to a circle at points $P$ and $Q$ on the circle intersect at a point $R$. If $P Q=6$ and $P R=5$, then the radius of the circle is
The two tangents to a circle from an external point are always
Two tangents drawn from the origin to the circle ${x^2} + {y^2} + 2gx + 2fy + c = 0$ will be perpendicular to each other, if
In the given figure, $AB$ is tangent to the circle with centre $O$ , the ratio of the shaded region to the unshaded region of the triangle $OAB$ is