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
If the centre of a circle is $(-6, 8)$ and it passes through the origin, then equation to its tangent at the origin, is
Tangents are drawn from $(4, 4) $ to the circle $x^2 + y^2 - 2x - 2y - 7 = 0$ to meet the circle at $A$ and $B$. The length of the chord $AB $ is
Let the lines $y+2 x=\sqrt{11}+7 \sqrt{7}$ and $2 y + x =2 \sqrt{11}+6 \sqrt{7}$ be normal to a circle $C:(x-h)^{2}+(y-k)^{2}=r^{2}$. If the line $\sqrt{11} y -3 x =\frac{5 \sqrt{77}}{3}+11$ is tangent to the circle $C$, then the value of $(5 h-8 k)^{2}+5 r^{2}$ is equal to.......
Circles $x^2 + y^2 + 4x + d = 0, x^2 + y^2 + 4fy + d = 0$ touch each other, if
The gradient of the normal at the point $(-2, -3)$ on the circle ${x^2} + {y^2} + 2x + 4y + 3 = 0$ is