The two tangents to a circle from an external point are always
Equal
Perpendicular to each other
Parallel to each other
None of these
The line $x\cos \alpha + y\sin \alpha = p$will be a tangent to the circle ${x^2} + {y^2} - 2ax\cos \alpha - 2ay\sin \alpha = 0$, if $p = $
From any point on the circle ${x^2} + {y^2} = {a^2}$ tangents are drawn to the circle ${x^2} + {y^2} = {a^2}{\sin ^2}\alpha $, the angle between them is
The tangent$(s)$ from the point of intersection of the lines $2x -3y + 1$ = $0$ and $3x -2y -1$ = $0$ to circle $x^2 + y^2 + 2x -4y$ = $0$ will be -
The equations of the tangents to the circle ${x^2} + {y^2} = 36$ which are inclined at an angle of ${45^o}$ to the $x$-axis are
The equation of the normal to the circle ${x^2} + {y^2} - 2x = 0$ parallel to the line $x + 2y = 3$ is