SOLUTION: PLEASE HELP ME WITH THIS FOUR PROBLEMS ABOUT WRITING AN EQUATION FOT THE CONIC SECTION THANK U I APPRECIATE YOUR SUPPORT I NEEDED FOR THIS MONDAY 24 ,JULY, 07 1. CIRCLE WITH CEN

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Question 89448: PLEASE HELP ME WITH THIS FOUR PROBLEMS ABOUT WRITING AN EQUATION FOT THE CONIC SECTION THANK U I APPRECIATE YOUR SUPPORT I NEEDED FOR THIS MONDAY 24 ,JULY, 07
1. CIRCLE WITH CENTER AT (4, -3) AND A RADIUS OF 8.
2. PARABOLA WITH VERTIX OF (2,-4) AND FOCUS OF ( 2,2).
3. ELIPSE WITH VERTIXES (-4,0) AND (4,0) AND CO-VERTICES (0,-9) AND (0,9).
4. HYPERBOLA WITH VERTICES (1,2) AND (5,2) AND FOCI (-1,2) AND (7,2).
THANK YOU!!!!!
Answer by stanbon(48569) (Show Source):
You can put this solution on YOUR website!
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.