Asosiy tarkibga o'tish

1.10-bo'lim : Umumiy grafiklar

18. Grafik kalkulyatordan foydalanmasdan \(\displaystyle {\left( {y + 2} \right)^2} - \frac{{{{\left( {x + 4} \right)}^2}}}{{16}} = 1\) grafigini chizing.

Yechim

Bu \(x\) atamasi oldida minus belgisi bo'lgan standart shakldagi giperbola va shuning uchun yuqoriga va pastga ochiladi. Giperbolaning markazi \(\left( { - 4, - 2} \right)\) da, ikkita tepasi \(\left( { - 4, - 1} \right)\) va \(\left( { - 4, - 3} \right)\) da, ikkita asimptotaning qiyaligi \( \pm \frac{1}{4}\) da.

Mana giperbolaning qisqacha chizmasi.

The graph of the hyperbola \({\left( {y + 2} \right)^2} - \frac{{{{\left( {x + 4} \right)}^2}}}{{16}} = 1\), drawn in solid red, along with its two asymptotes, drawn as dashed blue lines. The hyperbola is centered at (-4,-2) and opens up and down with vertices at (-4,-1) and (-4,-3). The asymptotes cross at the center with slopes \(\frac{1}{4}\) and \( - \frac{1}{4}\) and each branch of the hyperbola gets closer to them as it moves away from its vertex.