The gradient of the tangent line at the point $(a\cos \alpha ,a\sin \alpha )$ to the circle ${x^2} + {y^2} = {a^2}$, is
$\tan \alpha $
$\tan (\pi - \alpha )$
$\cot \alpha $
$ - \cot \alpha $
The normal at the point $(3, 4)$ on a circle cuts the circle at the point $(-1, -2)$. Then the equation of the circle is
The equation of the tangent to the circle ${x^2} + {y^2} - 2x - 4y - 4 = 0$ which is perpendicular to $3x - 4y - 1 = 0$, is
If the line $3x - 4y = \lambda $ touches the circle ${x^2} + {y^2} - 4x - 8y - 5 = 0$, then $\lambda $ is equal to
The slope of the tangent at the point $(h,h)$ of the circle ${x^2} + {y^2} = {a^2}$ is
Tangent to the circle $x^2 + y^2$ = $5$ at the point $(1, -2)$ also touches the circle $x^2 + y^2 -8x + 6y + 20$ = $0$ . Then its point of contact is