The lines $y - y_1 = m(x - x_1) \pm a \sqrt{1 + m^2}$ are tangents to the same circle. The radius of the circle is:

$A$ pair of tangents are drawn to the circle $x^2+y^2+6x-4y-12=0$ from a point $P(-4,-5)$. The area enclosed between these tangents and the circle is:

The equations of the tangents drawn from the origin to the circle ${x^2} + {y^2} - 2rx - 2hy + {h^2} = 0$ are

Match the points on the curve $2y^2 = x + 1$ with the slopes of the normals at those points and choose the correct answer.

$A. (7, 2)$	$1. -4\sqrt{2}$
$B. (0, 1/\sqrt{2})$	$2. -8$
$C. (1, -1)$	$3. 4$
$D. (3, \sqrt{2})$	$4. 0$
	$5. -2\sqrt{2}$

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

$A$ line makes equal intercepts on the coordinate axes and is tangent to the circle $x^2 + y^2 = 4$. The length of each intercept made by the line on the coordinate axes is ...