Cumberland County College Calculus Vertex Focus and Directrix Questions

  

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Section 11.4, 12.1, 12.2 and 12.3 Quiz
1) Find the center and the foci of the ellipse
(𝑥−3)2
16
+
(𝑦+3)2
1
= 1 and sketch the graph.
2) Find an equation for the ellipse with vertices V1(-1,-4) and V2(-1,6) and foci F1(-1,-3) and
F2(-1,5).
3) Find the vertex, focus and directrix of (x-3)2=8(y+1) and sketch the graph.
4) Find the center, vertices, foci and asymptotes of
(𝑥+2)2
9
−
(𝑦−3)2
16
= 1 and sketch the
graph.
5) Find the first four terms and the 100th term of an=n2-1
6) Find the first five terms of the recursive sequence an=2an-1+1 and a1=1
2
7) Find the first four partial sums and the nth partial sum of an=3𝑛.
8) Find the sums:
a. ∑4𝑘=1 𝑘 2
b. ∑12
𝑖=4 10
9) Find the common difference, the 5th term, the nth term and the 100th term of
-1,11,23,35,…
10) The 12th term is 118 and the 8th term is 146. Find the 1st and nth term.
11) Find the partial sum Sn when a=10, d= -8 and n=30
12) How many terms of the arithmetic sequence 12,20,28,… must be added to get 2700?
13) Determine the common ratio, the 5th term and the nth term of 7,
14) The 4th term is 12 and the 7th term is
2
1
32
9
. Find the 1st and nth term.
15) Find the partial sum Sn of a=3, r=3 and n=4
16) Find the sum ∑6𝑘=1 10(5)𝑘−1
14 27 56
, , ,…
3 9 27

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