If $m_1, m_2$ are the slopes of the tangents drawn from a point $(1, -3)$ to the circle $x^2+y^2-6x+4y+12=0$,then $9(m_1^2+m_2^2) = $

Suppose the angle between the tangents drawn from $(0,0)$ to the circle $(x+\lambda)^2+(y+1)^2=\lambda^2$ is $\frac{\pi}{2}$. Then,$\lambda$ satisfies

The equation of a circle which has a tangent $3x + 4y = 6$ and two normals given by $(x - 1)(y - 2) = 0$ is

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

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

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

If the line $3x + 4y - 1 = 0$ touches the circle $(x - 1)^2 + (y - 2)^2 = r^2$,then the value of $r$ will be