Answer to Question #86158 in Analytic Geometry for hitendra

Question

Find the vertices, eccentricity, foci and asymptotes of the hyperbola x2
8

Answer 1

I don't see equation of the hyperbola in the question. So, I present general way and you can substitute any numbers.

This is standard form of the equation of a hyperbola with center $(h,k)$ is

$$\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1.$$

The vertices are $(-a,0), \,\, (a,0)$.

To find the foci, we need the distance from the center to the foci $c^2=a^2+b^2$.

The foci are $(-c,0), (c,0)$.

The asymptotes are

$$\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=0 \Rightarrow y=\pm \dfrac{b}{a}(x-h)+k.$$