Persamaan garis singgung dengan gradien 1 pada hiperbola x2/100-y2/64=1 adalah....
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Jawab:
Penjelasan dengan langkah-langkah:
[tex]\displaystyle \frac{x^2}{100} - \frac{y^2}{64} = 1\to x = 10\cosh(t), y = 8\sinh(t)\\\\dy = 8\cosh(t), dx = 10\sinh(t)\to \frac{dy}{dx} = \dfrac{4}{5}\coth(t)\\\dfrac{4}{5}\coth(t)= 1\to \coth(t) = \dfrac{5}{4}\to \cosh(t) = \dfrac{5}{\sqrt{5^2-4^2}},\sinh(t) = \dfrac{4}{\sqrt{5^2-4^2}}\\\\\cosh(t) = \dfrac{5}{3},\sinh(t) = \dfrac{4}{3}\to x = \dfrac{50}{3}, y = \dfrac{32}{3}[/tex]
Garis singgungnya :
[tex]\displaystyle y = x+k \leftarrow \left( \frac{50}{3} ,\frac{32}{3} \right)\\k = \dfrac{32-50}{3}=-6\\\\\Huge{\boxed{\boxed{\boldsymbol{y=x-6}}}}[/tex]
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