Find the center and the vertices in the ellipse with equation \(\frac{{(x+2)}^2}{25} + \frac{{(y-3)}^2}{16} = 1.\)
Find the center and the vertices in the hyperbola with equation \(\frac{{(x-3)}^2}{36} - \frac{{(y-4)}^2}{25} = 1.\)
Write the equation in standard form for the hyperbola with the given characteristics:
C(-2, 1); a = 5; c = 8; vertical transverse axis.