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

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

1. A

$x-y-3=0$

2. B

$x-y+9=0$

3. C

$x-y+1=0$

4. D

$x-y+7=0$

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### Solution:

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

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

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

$\therefore$ Slope of the tangent is 1

$\therefore$ (i) becomes; $y=x±\sqrt{5-4}⇒y=x±1$

$⇒y=x+1$ or $y=x-1$

$⇒x-y+1=0$ or $x-y-1=0$

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