Noted that the equation of ellipse is given by $\dfrac{y^2}{a^2}+\dfrac{x^2}{b^2}=1$,where $b^2=a^2-c^2$ While the equation of hyperbola is $\dfrac{y^2}{a^2}-\dfrac{x^2}{b^2}=1$,where $b^2=c^2-a^2$
When substitute the the expression of $b^2$ into each equation
the ellipse equation
$\dfrac{y^2}{a^2}+\dfrac{x^2}{a^2-c^2}=1$
The hyperbola equation $\dfrac{y^2}{a^2}-\dfrac{x^2}{c^2-a^2}=1$ ,which is equivalent to $\dfrac{y^2}{a^2}+\dfrac{x^2}{a^2-c^2}=1$
So my conclusion is that hyperbola and ellipse are of the same formula, is my conclusion correct?