Asosiy tarkibga o'tish

1.10-bo'lim : Umumiy grafiklar

17. Grafik kalkulyatordan foydalanmasdan \(\displaystyle \frac{{{x^2}}}{{36}} - \frac{{{y^2}}}{{49}} = 1\) grafigini chizing.

Yechim

Bu \(y\) atamasi oldidagi minus belgisi bilan standart shakldagi giperbola bo'lib, o'ngga va chapga ochiladi. Giperbolaning markazi \(\left( {0,0} \right)\) da, ikkita tepasi \(\left( { - 6,0} \right)\) va \(\left( {6,0} \right)\) da, ikkita asimptotaning qiyaligi \( \pm \frac{7}{6}\) da.

Mana giperbolaning qisqacha chizmasi.

The graph of the hyperbola \(\frac{{{x^2}}}{{36}} - \frac{{{y^2}}}{{49}} = 1\), drawn in solid red, along with its two asymptotes, drawn as dashed blue lines. The hyperbola is centered at the origin and opens left and right with vertices at (-6,0) and (6,0). The asymptotes pass through the origin with slopes \(\frac{7}{6}\) and \( - \frac{7}{6}\) and each branch of the hyperbola gets closer to them as it moves away from its vertex.