The equation of a tangent to the hyperbola 4x2−5y2=20 parallel to the line x - y = 2 is

Given, equation of hyperbola is $\frac{x^{2}}{5} - \frac{y^{2}}{4} = 1$

Now, equation of the tangent to the hyperbola is $y = m x \pm \sqrt{a^{2} m^{2} - b^{2}}$ $\dots (i)$

Since, the tangent is parallel to $x - y = 2$

$∴$ Slope of the tangent is 1

$∴$ (i) becomes; $y = x \pm \sqrt{5 - 4} \Rightarrow y = x \pm 1$

$\Rightarrow y = x + 1$ or $y = x - 1$

$\Rightarrow x - y + 1 = 0$ or $x - y - 1 = 0$

The equation of a tangent to the hyperbola $4 x^{2} - 5 y^{2} = 20$ parallel to the line $x - y = 2$ is