Tangent to y² = 8x is y = mx + $\frac{2}{\mathrm{m}}$ also touches x² + y² = 2

 $\therefore \left|\frac{\frac{2}{\mathrm{m}}}{\sqrt{1+{\mathrm{m}}^2}}\right|=\sqrt{2}$

$\therefore$         m = ± 1

Tangent:  y = x + 2 and y = – x – 2

$\therefore$         point of intersection of tangents (–2, 0) $\equiv$ foot of directrix

Area = 2 $\left(\frac{1}{2}(1+4)\times 3\right)$ = 15