I need a bit of help solving the following conic section problems:
Write an equation of a parabola with the given info:
1) Vertex = (1, 2) Focus = (-1, 2)
2) Vertex = (2, 5) Focus = (2, 6)
Find the vertex, focus and directrix of each parabola:
3) y = 1/20 x ^ 2
4) x = y ^ 2 - 8y + 11
What are the foci, vertices and asymptote slope of the equations:
5) x ^ 2/16 + y ^ 2/ 9 = 1
6) 4x ^ 2 - y ^ 2 = 4
Write the equation of a hyperbola with the given info:
7) Vertices = (0, *plus or minus* 6) Foci = (0, *Plus or minus* 8)
8) Vertices = (*Plus or minus* 1, 3) Foci = (*Plus or minus* 3, 3)
Identify the conic section:
9) x ^ 2 + y ^ 2 - 6x - 8y + 16 = 0
10) x ^ 2 - y + 6x + 8 = 0
11) 4x ^ 2 + 9y ^ 2 - 24x - 36y + 36 = 0
12) 4x ^ 2 - y ^ 2 + 24x - 6y + 23 = 0
What is the major axis of:
13) 16x ^ 2 + 4y ^ 2 = 64
If you could help with all those, that would be AWESOME! :D

Quote:

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Originally Posted by ryoubakura98

I need a bit of help solving the following conic section problems:
Write an equation of a parabola with the given info:
1) Vertex = (1, 2) Focus = (-1, 2)
2) Vertex = (2, 5) Focus = (2, 6)
Find the vertex, focus and directrix of each parabola:
3) y = 1/20 x ^ 2
4) x = y ^ 2 - 8y + 11
What are the foci, vertices and asymptote slope of the equations:
5) x ^ 2/16 + y ^ 2/ 9 = 1
6) 4x ^ 2 - y ^ 2 = 4
Write the equation of a hyperbola with the given info:
7) Vertices = (0, *plus or minus* 6) Foci = (0, *Plus or minus* 8)
8) Vertices = (*Plus or minus* 1, 3) Foci = (*Plus or minus* 3, 3)
Identify the conic section:
9) x ^ 2 + y ^ 2 - 6x - 8y + 16 = 0
10) x ^ 2 - y + 6x + 8 = 0
11) 4x ^ 2 + 9y ^ 2 - 24x - 36y + 36 = 0
12) 4x ^ 2 - y ^ 2 + 24x - 6y + 23 = 0
What is the major axis of:
13) 16x ^ 2 + 4y ^ 2 = 64
If you could help with all those, that would be AWESOME! :D

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Identify the conic section:
9) x ^ 2 + y ^ 2 - 6x - 8y + 16 = 0 ----> circle with centre(3,4), radius = sqrt(84)
10) x ^ 2 - y + 6x + 8 = 0 -------------> parabola
11) 4x ^ 2 + 9y ^ 2 - 24x - 36y + 36 = 0 -----------> hyperbola, vertex at(3.2), symmetric to x-axis

12) 4x ^ 2 - y ^ 2 + 24x - 6y + 23 = 0 -------------->Hyperbola, symmetric to x-axis, vertex at (-3,-3)

Find the vertex, focus and directrix of each parabola:
3) y = 1/20 x ^ 2
Focus(0,5)
Directrix: y +5 =0
Vertex (0,0)

4) x = y ^ 2 - 8y + 11

Focus(1/4,0)
Directrix: x+1/4 =0
Vertex (5,4)

What are the foci, vertices and asymptote slope of the equations:
5) x ^ 2/16 + y ^ 2/ 9 = 1
Foci (sqrt(7), 0)
Vertices (0,0)

6) 4x ^ 2 - y ^ 2 = 4
Foci(sqrt(17),0)
Vertices (0,0)