Question

Choose the equation for the hyperbola centered at the origin with the given characteristics.

1.one focus (0, square root of 34), one vertex (0, 5)

2.vertical transverse axis, b = 6, c = square root of 45

3.vertices (+-2, 0), perimeter of central rectangle 24 units

Answer 1

I have multiple choice selections for these problems

Answer 2

The equation of a hyperbola that opens up/down (north/south) is
\[ \frac{y^2}{a^2}- \frac{x^2}{b^2} =1 \]
I remember that the y term goes first with "Y the smile? Y the frown?"

For
1.one focus (0, square root of 34), one vertex (0, 5)
we can plot these points

so we know we are looking for
\[ \frac{y^2}{a^2}- \frac{x^2}{b^2} =1 \]