Question

1. graph the hyperbola \\(\frac{x^2}{25} - \frac{y^2}{49} = 1\\). what are the vertices? \\((0, \pm7)\\) \\((\pm5, 0)\\) \\((0, \pm5)\\) \\((\pm7, 0)\\)

Explanation:

Step1: Identify hyperbola standard form

The given equation $\frac{x^2}{25}-\frac{y^2}{49}=1$ matches the horizontal transverse axis hyperbola form $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$.

Step2: Calculate value of $a$

From $a^2=25$, solve for $a$: $a=\sqrt{25}=5$.

Step3: Find vertices coordinates

For horizontal hyperbola, vertices are $(\pm a, 0)$, so substitute $a=5$: $(\pm5, 0)$.

Answer:

(±5, 0)