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The line 3 \mathrm x+5 \mathrm y=\mathrm k touches the ellipse  16 \mathrm x^2+25 \mathrm y^2=400   if  \mathrm k is

 

Option: 1

\pm \sqrt{5}


Option: 2

\pm \sqrt{15}


Option: 3

\pm 25


Option: 4

None of these


Answers (1)

best_answer

Putting 5 \mathrm y=\mathrm k-3 \mathrm x in the equation of the ellipse 16 \mathrm x^2+25 \mathrm y^2=400, we get

16 \mathrm{x}^2+(\mathrm{k}-3 \mathrm{x})^2=400

\Rightarrow \quad 25 \mathrm{x}^2-6 \mathrm{kx}+\mathrm{k}^2-400=0

Now    \mathrm{D}=0 \Rightarrow 36 \mathrm{k}^2-100\left(\mathrm{k}^2-400\right)=0

\Rightarrow \mathrm{k}= \pm 25
Hence (3) is the correct answer.

Posted by

Suraj Bhandari

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