Question:
The equation of a tangent to the hyperbola $4 x^{2}-5 y^{2}=20$ parallel to the line $x-y=2$ is :
Correct Option: , 3
Solution:
Hyperbola $\frac{x^{2}}{5}-\frac{y^{2}}{4}=1$
slope of tangent $=1$
equation of tangent $\mathrm{y}=\mathrm{x} \pm \sqrt{5-4}$
$\Rightarrow y=x \pm 1$
$\Rightarrow y=x+1$ or $y=x-1$