The length of the tangent drawn to the circle $x^2+y^2-2x+4y-11=0$ from the point $(1,3)$ is:

The equations of the tangents to the circle $x^2 + y^2 = 50$ at the points where the line $x + 7 = 0$ meets it,are

$A$ circle passes through the points $(-1, 1)$,$(0, 6)$,and $(5, 5)$. The point$(s)$ on this circle,the tangent$(s)$ at which is/are parallel to the straight line joining the origin to its centre is/are:

Two tangents to the circle $x^2+y^2=4$ at the points $A$ and $B$ meet at the point $P(-4,0)$. Then the area of the quadrilateral $PAOB$,where $O$ is the origin,is:

Consider the following statements:
Assertion $(A)$: The circle $x^2 + y^2 = 1$ has exactly two tangents parallel to the $x$-axis.
Reason $(R)$: $\frac{dy}{dx} = 0$ on the circle exactly at the points $(0, \pm 1)$.
Of these statements:

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