If $x^2+y^2=25$,then $\log _5[\max (3 x+4 y)]$ is

Let a circle $C_1$ be obtained by rolling the circle $x^2+y^2-4x-6y+11=0$ upwards $4$ units along the tangent $T$ to it at the point $(3,2)$. Let $C_2$ be the image of $C_1$ in $T$. Let $A$ and $B$ be the centers of circles $C_1$ and $C_2$ respectively,and $M$ and $N$ be respectively the feet of perpendiculars drawn from $A$ and $B$ on the $x$-axis. Then the area of the trapezium $AMNB$ is:

If the chord joining the points $(1,2)$ and $(2,-1)$ on a circle subtends an angle of $\frac{\pi}{4}$ at any point on its circumference,then the equation of such a circle is:

The area (in sq. units) of the region bounded by the circle $x^2+y^2=64$,positive $x$-axis and the line $y=\sqrt{3}x$ is

If $(1, a)$ and $(b, 2)$ are conjugate points with respect to the circle $x^2+y^2=25$,then $4a+2b=$

If the lines $3x - 4y + 4 = 0$ and $6x - 8y - 7 = 0$ are tangents to the same circle,then the area of that circle (in sq. units) is