Question

equation of hyperbola with foci on y axis

Answer 1

$\frac{ {x}^{2} }{ {a}^{2} } - \frac{ {y}^{2} }{ {b}^{2} } = - 1$
This is the equation.

Answer 2

Answer:

$\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$

Or

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

Step-by-step explanation:

The standard equation of a hyperbola that has its foci on the y-axis and centre at the origin is given by:

$\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$

This hyperbola has no x-intercepts.

The y-intercept is at: $\pm a$

The foci has coordinates: $F=(0,\pm c)$

where

$c^2=a^2+b^2$

If this hyperbola is translated so that its center is now at: (h,k);

Then the equation becomes:

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