The length of the tangent drawn from the mid-point of the line joining the origin and the point $(4, -4)$ to the circle $2x^2 + 2y^2 - y = 0$ is

The area (in sq. units) of the triangle formed by the $X$-axis,the tangent,and the normal drawn to the circle $x^2+y^2=10x$ at the point $(9,3)$ is

$A$ is the centre of the circle $x^2+y^2-2x-4y-20=0$. If the tangents drawn at the points $B(1,7)$ and $D(4,-2)$ on the circle meet at the point $C$,then the area of the quadrilateral $ABCD$ (in square units) is

If the line $x = 7$ touches the circle ${x^2} + {y^2} - 4x - 6y - 12 = 0$,then the coordinates of the point of contact are:

The equation of the normal at $t=\frac{\pi}{2}$ to the curve $x=2 \sin t, y=2 \cos t$ is

The tangent$(s)$ from the point of intersection of the lines $2x - 3y + 1 = 0$ and $3x - 2y - 1 = 0$ to the circle $x^2 + y^2 + 2x - 4y = 0$ will be -