HIPERBOLA-PERSAMAAN GARIS SINGGUNG (IRISAN KERUCUT)

 Perhatikan tabel berikut

$\begin{array}{|l|l|l|}\hline \begin{aligned}&\textrm{Persamaan}\\&\textrm{hiperbola}\end{aligned}&\qquad \displaystyle \frac{x^{\displaystyle 2}}{a^{\displaystyle 2}}-\displaystyle \frac{y^{\displaystyle 2}}{b^{\displaystyle 2}}=1&\qquad \displaystyle \frac{(x-h)^{\displaystyle 2}}{a^{\displaystyle 2}}-\displaystyle \frac{(y-k)^{\displaystyle 2}}{b^{\displaystyle 2}}=1\\\hline   \begin{aligned}&\textrm{dengan}\\ &\textrm{gradien}\;\: m\end{aligned}&y=mx \pm \sqrt{a^{\displaystyle 2}m^{\displaystyle 2}-b^{\displaystyle 2}}&y-k=m(x-h)\pm \sqrt{a^{\displaystyle 2}m^{\displaystyle 2}-b^{\displaystyle 2}}\\\hline \begin{aligned}&\textrm{di titik}\\ &\left( x_{1},y_{1} \right)\\ &\textrm{pada }\\ &\textrm{hiperbola} \end{aligned}&\quad\displaystyle \frac{x_{1}x}{a^{\displaystyle 2}}-\frac{y_{1}y}{b^{\displaystyle 2}}=1&\displaystyle \frac{\left( x_{1}-h \right)(x-h)}{a^{\displaystyle 2}}-\frac{\left( y_{1}-k \right)\left( y-k \right)}{b^{\displaystyle 2}}=1\\\hline \begin{aligned}&\textrm{melalui}\\ &\textrm{titik}\\ &\left( x_{1},y_{1} \right)\\ &\textrm{di luar}\\ &\textrm{hiperbola}\\ &\\ &\\ &\\ &\\ &\\ &\\ &\\ &\\ &\\ &\\ &\\ &\\ &\\ &\\ &\\ &\\ &\\\end{aligned}&\begin{aligned}&\textrm{Prosesnya}:\\\\ &Pertama:\\ &\textrm{cari persamaan garis}\\ &\textrm{kutubnya (polar)}\\ &\textrm{dengan rumus pada}\\ &\textrm{baris 3 kolom 2}\\ &\textrm{di tabel ini}\\\\ &Kedua:\\ &\textrm{Potongkan garis kutub}\\ &\textrm{dengan hiperbola di titik}\\ &A\left( x_{A},y_{A} \right)\: \textrm{dan di titik}\\ &B\left( x_{B},y_{B} \right)\\\\ &Ketiga:\\ &\textrm{Persamaan garis}\\ &\textrm{singgung yang dicari}:\\ &\displaystyle \frac{x_{A}x}{a^{\displaystyle 2}}-\frac{y_{A}y}{b^{\displaystyle 2}}=1\\ & \textrm{dan}\\ &\displaystyle \frac{x_{B}x}{a^{\displaystyle 2}}-\frac{y_{B}y}{b^{\displaystyle 2}}=1 \end{aligned}&\begin{aligned}&\textrm{Prosenya kurang lebih sama}\\ &\textrm{dengan proses sebelah kiri}\\ &\textrm{tersebut}\\ &\\ &\\ &\\ &\\ &\\ &\\ &\\ &\\ &\\ &\\ &\\ &\\ &\\ &\\ &\\ &\\ &\\ &\\ &\\ \end{aligned}\\\hline  \end{array}$.

$\LARGE{CONTOH SOAL}$.