In a book consisting of 600 pages, there are 60 typographical errors. The probability that a randomly chosen page will contain at most two errors, is

If $M$ is the foot of the perpendicular drawn from the origin $O$ on to the variable line $L$, passing through a fixed point $(a, b)$, then the locus of the mid-point of $O M$ is

When the origin is shifted to the point $\left(\frac{3}{2}, \frac{3}{2}\right)$ by the translation of coordinate axes, then the transformed equation of $32 x^2+8 x y+32 y^2-108 x-108 y+99=0$ is

A line $L_1$ passing through $A(3,4)$ and having slope 1 cuts another line $L_2$ passing through $C$ at $B$, such that $A B=A C$. If the equation of line $B C$ is $2 x-y+4=0$, then the equation of $A C$ is