4.4-bo'lim: Giperbolalar

1-3-masalalar uchun giperbolaning eskizini tuzing.

1. \( \displaystyle \frac{{{y^2}}}{{16}} - \frac{{{{\left( {x - 2} \right)}^2}}}{9} = 1\) Yechim
2. \( \displaystyle \frac{{{{\left( {x + 3} \right)}^2}}}{4} - \frac{{{{\left( {y - 1} \right)}^2}}}{9} = 1\) Yechim
3. \( \displaystyle 3{\left( {x - 1} \right)^2} - \frac{{{{\left( {y + 1} \right)}^2}}}{2} = 1\) Yechim

4 va 5-masalalar uchun tenglamaning \(x\) va \(y\) qismlaridagi kvadratni to'ldiring va tenglamani giperbola tenglamasining standart shakliga yozing.

1. \(4{x^2} - 32x - {y^2} - 4y + 24 = 0\) Yechim
2. \(25{y^2} + 250y - 16{x^2} - 32x + 209 = 0\) Yechim