$E: \frac{x^2}{4^2}+\frac{y^2}{3^2}=1$

$$\begin{aligned} & T: y=m x \pm \sqrt{16 m^2+9} \\ & y=x+p \\ & \Rightarrow m=1 \\ & \Rightarrow p= \pm \sqrt{16+9} \\ & = \pm 5 \end{aligned}$$

$T: y=x \pm 5$ will to cut the $E$ at $A\left(-\frac{16}{5}, \frac{9}{5}\right)$

$$B\left(\frac{16}{5},-\frac{9}{5}\right)$$

Also, $y=x$ will cut the $E$ at $C\left(\frac{12}{5}, \frac{12}{5}\right)$

$$D\left(-\frac{12}{5},-\frac{12}{5}\right)$$

$A B C D$ in not give in cyclic order

$\therefore$ it does not form any quadrilateral

$\therefore \quad$ No option should match

If order is not considered then

Area $=24$ sq. unit.