The angle between the pair of tangents from the point $(1, 1/2)$ to the circle $x^2 + y^2 + 4x + 2y -4=0$ is-
${\cos ^{ - 1}}\frac{4}{5}$
${\sin ^{ - 1}}\frac{4}{5}$
${\sin ^{ - 1}}\frac{3}{5}$
None of these
The equation to the tangents to the circle ${x^2} + {y^2} = 4$, which are parallel to $x + 2y + 3 = 0$, are
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:
Equation of the tangent to the circle ${x^2} + {y^2} = {a^2}$ which is perpendicular to the straight line $y = mx + c$ is
If the line $3x -4y -k = 0 (k > 0)$ touches the circle $x^2 + y^2 -4x -8y -5 = 0$ at $(a, b)$ then $k + a + b$ is equal to :-
The line $lx + my + n = 0$ will be a tangent to the circle ${x^2} + {y^2} = {a^2}$ if