Question

Find an equation in standard form for the hyperbola with vertices at (0, ±3) and foci at (0, ±7)

Answer 1

It will look like this:

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

A quick look at the vertices and foci suggests h = k = 0

Now it looks like this

\(\dfrac{x^{2}}{a^{2}}-\dfrac{y^{2}}{b^{2}} = 1\)

Another quick look at the vertices give a = 3

Now, it looks like this:

\(\dfrac{x^{2}}{3^{2}}-\dfrac{y^{2}}{b^{2}} = 1\)

Of course, this is not "Standard" form, but there is only on question left to answer. How can the vertices and foci help us fin 'b'?

Answer 2

so would it be y^2/49 - x^2/9

Answer 3

1) You changed the orientation of the hyperbola. That's no good.
2) You used the foci distance for the co-vertex distance. That's no good.
3) It doesn't equal anything. Thus, it's not an equation or relation, just a statement,

Let's get back to where I left off. No more guessing.

4) You should have a relationship between a, b, and c for an hyperbola. What is it.