The normal drawn at $(1,1)$ to the circle $x^2+y^2-4x+6y-4=0$ is

If the centre of a circle is $(-6, 8)$ and it passes through the origin,then the equation of its tangent at the origin is

$x-2y-6=0$ is a normal to the circle $x^2+y^2+2gx+2fy-8=0$. If the line $y=2$ touches this circle,then the radius of the circle can be

Consider a circle $(x-\alpha)^2+(y-\beta)^2=50$,where $\alpha, \beta > 0$. If the circle touches the line $y+x=0$ at the point $P$,whose distance from the origin is $4 \sqrt{2}$,then $(\alpha+\beta)^2$ is equal to................

The square of the length of the tangent drawn from the point $(\alpha, \beta)$ to the circle $ax^2 + ay^2 = r^2$ is

The angle between the tangents drawn from the origin to the circle $(x-7)^2+(y+1)^2=25$ is