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

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

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Solution:

Hyperbola $\frac{x^{2}}{5} - \frac{y^{2} }{4} = 1 $
slope of tangent = $1$
equation of tangent $y = x \pm \sqrt{5 - 4}$
$\Rightarrow \; y = x \pm 1$
$\rightarrow \; y = x + 1$ or $y = x - 1$