A function $f: \mathbf{R} \rightarrow \mathbf{R}$ is such that $f(\mathrm{l})=2$ and $f(x+y)=f(x) \cdot f(y) \forall x, y$. The area (in square units) enclosed by the lines $2|x|+5|y| \leq 4$ expressed interms of $f(1), f(2)$ and $f(4)$ is

Two straight lines $3 x+4 y=5$ and $4 x-3 y=15$ intersect at the point $A$. The equations of the lines passing through $(1,2)$ and intersecting the given lines at $B$ and $C$ such that $A B=A C$ are

The equation of a line making an angle $60^{\circ}$ with the line $x+y-3=0$ and passing through the point $(1,1)$ is

Let $P$ be the pair of lines represented by $2 x^2-5 x y+2 y^2+6 x-3 y=0$ and consider the following independent statements

(i) $\alpha$ is the $x$ coordinate of the point of intersection of the pair of lines $P$.

(ii) $\beta$ is the slope of one of the lines of $P$ passing through origin.

(iii) $\gamma$ is the constant term in the equation of the pair of angular bisectors of $P$.

Then,