The equations of the tangent to the circle $5x^2 + 5y^2 = 1$ parallel to the line $3x + 4y = 1$ are

The angle of intersection between the curves $y=[|\sin x|+|\cos x|]$ and $x^{2}+y^{2}=10,$ where $[x]$ denotes the greatest integer $\leq x,$ is

Let the lines $(2-i)z = (2+i)\bar{z}$ and $(2+i)z + (i-2)\bar{z} - 4i = 0$ (where $i^2 = -1$) be normal to a circle $C$. If the line $iz + \bar{z} + 1 + i = 0$ is tangent to this circle $C$,then its radius is

Let $AB$ be a chord of length $12$ of the circle $(x-2)^{2}+(y+1)^{2}=\frac{169}{4}$. If tangents drawn to the circle at points $A$ and $B$ intersect at the point $P$,then five times the distance of point $P$ from chord $AB$ is equal to $.......$

If the lines $3x + 4y - 14 = 0$ and $6x + 8y + 7 = 0$ are both tangents to a circle,then its radius is

The equation of the tangent to the circle,given by $x=5 \cos \theta, y=5 \sin \theta$ at the point $\theta=\frac{\pi}{3}$ on it,is