That's more than a couple of problems. Having that many problems in one thread is generally frowned upon here.
where (h, k) is the vertex and p is the focal length. Since the y-term is squared, the parabola opens either to the left or to the right, which means that the focus would be at point
and the directrix would be the equation
The equation for the ellipse is usually written in one of 2 forms:Find the center, foci, and vertices of the ellipse.
4x2 + 5y2 - 24x + 60y + 196 = 0
See this site for more info: Conics: Ellipses: Introduction .
To make the problem look like one of the two forms above, you'll need to complete the square.
Rearrange the terms first.
Factor out the common factor:
From here, complete the square. (I assume you know how to do this.) Then divide both sides by the number you'll end up with on the right side. The center is at (h, k). Consult the site I linked above to find the vertices and foci.
Your hyperbola equation is missing.