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:

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

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:

For what value of $\lambda$ does the line $3x - 4y = \lambda$ touch the circle $x^2 + y^2 - 4x - 8y - 5 = 0$?

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

If the equation of the common tangent at the point $(1, -1)$ to the two circles,each of radius $13$,is $12x + 5y - 7 = 0$,then the centers of the two circles are