Question

This hyperbola is centered at theorigin. Find its equation.Foci: (-2,0) and (2,0)Vertices: (-1,0) and (1,0)

Answer 1

From the question, the center of the hyperbola is

`\begin{gathered} (h,k),\text{ which is } \\ (0,0) \end{gathered}`

a is the distance between the center to vertex, which is -1 or 1, and

c is the distance between the center to foci, which is -2 or 2.

b is given as

`\begin{gathered} b^2=c^2-a^2 \\ b^2=2^2-1^2 \\ b=\sqrt[]{3} \end{gathered}`

But equation of a hyperbola is given as

`((x-h)^2)/(a^2)-((y-k)^2)/(b^2)=1`

Substituting the values of a, b, h and k, we have

`\begin{gathered} ((x-0)^2)/(1^2)-\frac{(y-0)^2}{\sqrt[]{3}^2}=1 \\ (x^2)/(1)-(y^2)/(3)=1 \end{gathered}`

Hence the answer is

`(x^2)/(1)-(y^2)/(3)=1`