The area of triangle formed by the lines x - y = 0, x + y = 0 and...

Equation of the tangent to the hyperbola $x^{2} - y^{2} = 16$ in parametric form is
$4xsec ϕ - 4ytan ϕ = 16$
$⇒ xsec ϕ - ytan ϕ = 4$
Solving with $y = x and y = - x$, we get,
$A\left(4\left(sec ϕ + tan ϕ\right), 4\left(sec ϕ + tan ϕ\right)\right),$
B \left(4 \left(sec ϕ - tan ϕ\right),4\left(tan ϕ - sec ϕ\right)\right)$<br />$∴$Area bounded by$∆ AOB$<br />$= \left|\dfrac{1}{2}\l$lleft(16\left(\tan^{2} ϕ - \sec^{2} ϕ\right)$- 16\left(\sec^{2} ϕ - \tan^{2} ϕ\right)\right)|$<br />$= \left|\dfrac{1}{2}\left(-16 - 16\right)\right| = 16& sq.& units