4.4-bo'lim : Giperbolalar

1-5-masalalar uchun giperbolaning eskizini tuzing.

1. \( \displaystyle \frac{{{x^2}}}{9} - \frac{{{y^2}}}{4} = 1\)
2. \( \displaystyle \frac{{{{\left( {y + 3} \right)}^2}}}{{36}} - \frac{{{{\left( {x + 2} \right)}^2}}}{{16}} = 1\)
3. \( \displaystyle \frac{{{{\left( {y - 5} \right)}^2}}}{{49}} - \frac{{{x^2}}}{{64}} = 1\)
4. \( \displaystyle 9{\left( {x - 4} \right)^2} - \frac{{{{\left( {y - 1} \right)}^2}}}{4} = 1\)
5. \( \displaystyle \frac{1}{{25}}{\left( {y + 1} \right)^2} - 15{\left( {x - 3} \right)^2} = 1\)

6-8-masalalar uchun tenglamaning \(x\) va \(y\) qismlaridagi kvadratni to'ldiring va tenglamani giperbola tenglamasining standart shakliga yozing.

1. \(9{x^2} - 4{y^2} + 48y - 180 = 0\)
2. \({y^2} - 6y - 4{x^2} - 8x - 11 = 0\)
3. \(7{x^2} - 28x - 4{y^2} + 40y - 100 = 0\)