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6. For each of the following ellipses, find the coordinates of the center, vertices, and foci; the lengths of the major and minor axes; the eccentricity; and the equations of the directrices. Sketch the curve.
(a) [tex]$\frac{x^2}{16}+\frac{y^2}{4}=1$[/tex]
(b) [tex]$25x^2 + 9y^2 = 225$[/tex]
(c) [tex]$x^2 + 9y^2 + 4x - 18y - 23 = 0$[/tex]
7. Find the equation of the ellipse, given:
(a) Vertices [tex]$(\pm 8, 0)$[/tex], minor axis [tex]$= 6$[/tex]
(b) One vertex at [tex]$(0, 13)$[/tex], one focus at [tex]$(0, -12)$[/tex], and center at [tex]$(0, 0)$[/tex]
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