The circle $x^2 + y^2 - 3x - 4y + 2 = 0$ cuts the $x$-axis at

The centre of the circle $(x - x_1)(x - x_2) + (y - y_1)(y - y_2) = 0$ is

The number of integral values of $\lambda$ for which $x^2 + y^2 + \lambda x + (1 - \lambda)y + 5 = 0$ is the equation of a circle whose radius cannot exceed $5$ is:

In $\triangle ABC$,$\angle A = 90^{\circ}$ and the coordinates of points $B$ and $C$ are $(2, -4)$ and $(1, 5)$. Then the equation of the circumcircle of $\triangle ABC$ is

The radius of the circle $r = \sqrt{3} \sin \theta + \cos \theta$ is

If the equation of the circle lying in the first quadrant,touching both the coordinate axes and the line $\frac{x}{3}+\frac{y}{4}=1$ is $(x-c)^2+(y-c)^2=c^2$,then $c=$