The equation of the tangent to the circle $x^2 + y^2 = r^2$ at the point $(a, b)$ is $ax + by - \lambda = 0$,where $\lambda$ is:

The angle between the two tangents drawn from the point $(\alpha, \beta)$ to the circle $x^{2} + y^{2} = a^{2}$ is:

If $m_1, m_2$ are the slopes of the tangents drawn through the point $(-1, -2)$ to the circle $(x-3)^2 + (y-4)^2 = 4$,then $\sqrt{3}|m_1 - m_2| = $

The equation of the normal to the circle $x^2+y^2-2x+4y-5=0$ at the point $(2,1)$ is:

When is the line $lx + my + n = 0$ a tangent to the circle $x^2 + y^2 = r^2$?

If the tangents at the points $P$ and $Q$ on the circle $x^2 + y^2 - 2x + y = 5$ meet at the point $R \left(\frac{9}{4}, 2\right)$,then the area of the triangle $PQR$ is