If the line $x+y=0$ touches the curve $ax^2 = 2y^2 - b$ at $(1, -1)$,then the values of $a$ and $b$ are respectively:

If $y = c$ is a tangent to the circle $x^2 + y^2 - 2x + 2y - 2 = 0$ at the point $(1, 1)$,then the value of $c$ is:

$A$ 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:

If the straight line $4x + 3y + \lambda = 0$ touches the circle $2(x^2 + y^2) = 5$,then $\lambda$ 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.

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

The slope of the common tangent drawn to the circles $x^2+y^2-4x+12y-216=0$ and $x^2+y^2+6x-12y+36=0$ is