Math, asked by ItzAshi, 6 hours ago

Show that the line y = x + √7 touches the hyperbola 9x² – 16y² = 144

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Answered by XxItzAdyashaxX
31

Answer:

 \mathcal  {ANSWER}

➡The line may touch the hyperbola.

y = mx +  \sqrt{ {a}^{2}  {m}^{2}  -  {b}^{2} }  \:  \:  \: be \: the \: equation.

and \: condition \: is \: c =  +  \sqrt{ {a}^{2}  {m}^{2} -  {b}^{2}  }

 \sqrt{7}  =  +  \sqrt{16 \times  {1}^{2} \:  - 9 }  \\

 \sqrt{7}  =  +  \sqrt{16 - 19}  \\

 \sqrt{7}  =  +  \sqrt{7}  \\ hence \: proved. \\

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Answered by ItzAshleshaMane
20

This is your answer.

Hope it will help you..

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