The equation of a tangent to the hyperbola

Question:

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

  1. $x-y+9=0$

  2. $x-y+7=0$

  3. $x-y+1=0$

  4. $x-y-3=0$


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 $y=x-1$

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