Question 89448
For each of these you should draw the picture so you see how vertices, foci,radius, etc. relate to one another.
1. CIRCLE WITH CENTER AT (4, -3) AND A RADIUS OF 8.
(x-4)^2+(y+3)^2 = 64
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2. PARABOLA WITH VERTIX OF (2,-4) AND FOCUS OF ( 2,2).
Form: (x-h)^2 = 4p(y-k)
(x-2)^2 = 4*6(y+4)
x^2-4x+4 = 24y+96
x^2-4x-92 = 24y
y = (1/24)x^2 -(1/6)x-(23/6)
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3. ELIPSE WITH VERTIXES (-4,0) AND (4,0) AND CO-VERTICES (0,-9) AND (0,9).
x^2/16 + y^2/81 = 1
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4. HYPERBOLA WITH VERTICES (1,2) AND (5,2) AND FOCI (-1,2) AND (7,2). 
Form: (x-h)^2/a^2 - (y-k)^2/b^2 = 1
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Vertices at (1,2),(5,2) implies center is at (3,2)
Center at (3,2)and vertex at (5,2) implies a=2
Center at (3,2) and focus at (7,2) implies c=4
For ellipe b^2=c^2-a^2
b^2 = 4^2-2^2 = 12
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EQUATION:
(x-3)^2/4 - (y-2)^2/12 = 1
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Cheers,
stan H.