PreCalc – Worksheet 7.5
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Section 1: Parabolas
1) Find the vertex, focus, and directrix. Then graph. (𝑥 − 4)2 = 12(𝑦 − 1)
2) Find the vertex, focus, and directrix. Then graph. (𝑥 + 5)2 = −8(𝑦 − 2)
3) Find the vertex, focus, and directrix. Then graph. (𝑦 + 3)2 = 4(𝑥 + 7)
4) Find the vertex, focus, and directrix. Then graph. 𝑦 2 = −16𝑥
5) Find the vertex, focus, and directrix. Then graph. 𝑥 2 + 8𝑥 − 4𝑦 = 0
6) Find the vertex, focus, and directrix. Then graph. 𝑦 2 + 10𝑦 + 8𝑥 − 7 = 0
7) Find the equation of a parabola with vertex (3, -6) and focus (3, 0).
8) Find the equation of a parabola with focus (-4, -1) and directrix 𝑥 = −2.
Section 2: Circles
6) Find the equation of a circle with center (4, -7) and radius = 11.
7) Find the equation of a circle with center (0, 0) and radius = 3√5.
8) Find the equation of a circle with center (-1, 5) and that goes through the point (9, 29).
9) Find the equation of the circle, as well as the center and the radius: 𝑥 2 + 14𝑥 + 𝑦 2 − 10𝑦 − 7 = 0
10) Find the equation of the circle, as well as the center and the radius: 11 + 𝑦 2 − 2𝑥 + 𝑥 2 + 22𝑦 = 0
Section 3: Ellipses
11) Find the center, vertices, and foci, then graph:
𝑥2
36
+
(𝑦+8)2
9
=1
12) Find the center, vertices, and foci, then graph: 25𝑥 2 + 4𝑦 2 = 100
13) Find the center, vertices, and foci, then graph: 3𝑥 2 + 𝑦 2 + 18𝑥 − 2𝑦 − 8 = 0
14) Find the standard form of the ellipse given in the graph:
15) Find the standard form of the ellipse given this information: Foci at (-2, 3) and (-2, 11), and major axis has
length = 18.
Section 4: Limits
16) lim− 𝑓(𝑥) =
𝑥→1
17) lim+ 𝑓(𝑥) =
𝑥→1
18) lim 𝑓(𝑥) =
𝑥→1
19) 𝑓(1) =
20) lim− 𝑓(𝑥) =
𝑥→0
21) lim+ 𝑓(𝑥) =
𝑥→0
22) lim 𝑓(𝑥) =
𝑥→0
23) 𝑓(0) =
24) lim 𝑓(𝑥) =
𝑥→−1
25) lim 𝑓(𝑥) =
𝑥→3