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]
(c) Foci [tex]( \pm 10,0)[/tex], eccentricity [tex]=\frac{5}{6}[/tex]
(d) Vertices [tex](8,3)[/tex] and [tex](-4,3)[/tex], one focus at [tex](6,3)[/tex]
(e) Directrices [tex]4y-33=0, 4y+17=0[/tex]; major axis on [tex]x+1=0[/tex]; eccentricity [tex]=\frac{4}{5}[/tex]
8. For each of the following hyperbolas, find:
- Coordinates of the center, vertices, and foci
- Lengths of the transverse and conjugate axes
- Eccentricity
- Equations of the directrices and asymptotes
- Sketch the locus
(a) [tex]\frac{x^2}{16}-\frac{y^2}{4}=1[/tex]
(b) [tex]25y^2-9x^2=225[/tex]
(c) [tex]9x^2-4y^2-36x+32y+8=0[/tex]
9. Find the equation of the hyperbola, given:
(a) Center [tex](0,0)[/tex], vertex [tex](4,0)[/tex], focus [tex](5,0)[/tex]
(b) Center [tex](0,0)[/tex], focus [tex](0,-4)[/tex], eccentricity [tex]=2[/tex]
(c) Center [tex](0,0)[/tex], vertex [tex](5,0)[/tex], one asymptote [tex]5y+3x=0[/tex]
(d) Vertices [tex](-11,1)[/tex] and [tex](5,1)[/tex], one asymptote [tex]x-4y+7=0[/tex]
(e) Transverse axis parallel to the [tex]x[/tex]-axis, asymptotes [tex]3x+y-7=0[/tex] and [tex]3x-y-5=0[/tex], passes through [tex](4,4)[/tex]
