If the sides of a rectangle are given by the equations $x=-2, x=6, y=-2, y=5$, then the equation of the circle, drawn on the diagonal of this rectangle as its diameter, is

The solution set of the equation $\tan x+\sec x=2 \cos x$, in the interval $[0,2 \pi]$ is

If one of the lines represented by $a x^2+2 h x y+b y^2=0$ is perpendicular to $\mathrm{m} x+\mathrm{n} y=18$, then

If $\sin ^{-1}\left(\frac{x}{13}\right)+\operatorname{cosec}^{-1}\left(\frac{13}{12}\right)=\frac{\pi}{2}$, then the value of