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The equation of a tangent to the hyperbola \mathrm{4 x^2-5 y^2=20} parallel to the line \mathrm{x-y=3} is

Option: 1

\mathrm{x-y-3=0}


Option: 2

\mathrm{x-y+9=0}


Option: 3

\mathrm{x-y+1=0}


Option: 4

\mathrm{x-y+7=0}


Answers (1)

best_answer

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

Now, equation of the tangent to the hyperbola is

\mathrm{ y=m x \pm \sqrt{a^2 m^2-b^2} }                             ....(1)

Since, the tangent is parallel to \mathrm{x-y=3}

 

\mathrm{ \begin{aligned} & \therefore \text { Slope of the tangent is } 1 \\\\ & \therefore \text { (i) becomes; } y=x \pm \sqrt{5-4} \Rightarrow y=x \pm 1 \\\\ & \Rightarrow y=x+1 \text { or } y=x-1 \\\\ & \Rightarrow x-y+1=0 \text { or } x-y-1=0 \end{aligned} }

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