The equations of the tangents drawn from the origin to the circle ${x^2} + {y^2} - 2rx - 2hy + {h^2} = 0$ are
$x = 0,y = 0$
$({h^2} - {r^2})x - 2rhy = 0,x = 0$
$y = 0,x = 4$
$({h^2} - {r^2})x + 2rhy = 0,x = 0$
Tangents $AB$ and $AC$ are drawn from the point $A(0,\,1)$ to the circle ${x^2} + {y^2} - 2x + 4y + 1 = 0$. Equation of the circle through $A, B$ and $C$ is
Tangents are drawn from the point $(-1,-4)$ to the circle $x^2 + y^2 - 2x + 4y + 1 = 0$. Length of corresponding chord of contact will be-
The set of all values of $a^2$ for which the line $x + y =0$ bisects two distinct chords drawn from a point $P\left(\frac{1+a}{2}, \frac{1-a}{2}\right)$ on the circle $2 x ^2+2 y ^2-(1+ a ) x -(1- a ) y =0$ is equal to:
If a line passing through origin touches the circle ${(x - 4)^2} + {(y + 5)^2} = 25$, then its slope should be
The angle between the tangents to the circle ${x^2} + {y^2} = 169$ at the points $(5, 12) $ and $(12, -5)$ is ............. $^o$