Unit 2: Conics HOMEWORK
Introduction to Analysis Honors
Lesson 1 - Circles
rite the standard form of the equation and the general form of the equation of the circle of radiusrand
W
center(ℎ, 𝑘).
1. 𝑟 = 5
(ℎ, 𝑘) = (4, − 3)
2
2
2. 𝑥 + 𝑦 = 4
a) Center: ________
b) Graph:
c) x-intercepts:
Radius: ________
y-intercepts:
2
2
3. 𝑥 + (𝑦 − 1) = 1
a) Center: ________
b) Graph:
c) x-intercepts:
Radius: ________
y-intercepts:
2
2
4. 𝑥 + 𝑦 − 6𝑥
+ 2𝑦
+ 9 = 0
c) x-intercepts:
a) Center: ________
b) Graph:
Radius: ________
y-intercepts:
2
2
+ 2𝑦
− 20 = 0
5. 𝑥 + 𝑦 + 4𝑥
c) x-intercepts:
a) Center: ________
b) Graph:
Radius: ________
y-intercepts:
2
2
6. Find an equation of the tangent line to the circle(𝑥 + 2) + (𝑦 + 3) = 58at the point(1, 4) . Write
your answer in𝑦 = 𝑚𝑥 + 𝑏form.
Unit 2: Conics HOMEWORK
Introduction to Analysis Honors
Lesson 2 - Ellipses Day 1
Match each graph of an ellipse to its equation:
1.
2.
3.
4.
2
2
𝑥
A) 4 + 𝑦 = 1
2
2
𝑦
B)𝑥 + 4 = 1
2
𝑥
2
𝑦
C) 16 + 4 = 1
2
𝑥
2
𝑦
D) 4 + 16 = 1
Find the center, vertices, co-vertices and foci of each ellipse. Graph each equation by hand.
5.
2
2
𝑥
𝑦
+ 4
25
2
2
= 1
+ 𝑦 = 16
6. 4𝑥
Write the equation of the ellipse.
7. Center at(0, 0)
Focus at(3, 0)
Vertex at(5, 0)
8. Center at(0, 0)
Focus at(0, − 4)
Vertex at(0, 5)
9. Foci at(± 2, 0) ;
Length of major axis is 6
Unit 2: Conics HOMEWORK
Introduction to Analysis Honors
Lesson 3 - Ellipses Day 2
nalyze each equation: find the center, vertices, co-vertices and foci of each ellipse. Graph each equation
A
by hand.
1.
2
(𝑥−3)
4
2
+
(𝑦+
1)
9
2
2
= 1
2. 9𝑥
+ 4𝑦
− 18𝑥 + 16𝑦 − 11 = 0
Find the equation for each ellipse.
3. Center at(2, − 2)
Vertex at(7, − 2)
Focus at (4,-2)
4. Foci at(5, 1) and(− 1, 1)
Length of major axis is 8
Applications and extensions.
5. Semielliptical Arch Bridge:An arch in the shape ofthe upper half of an ellipse is used to support a
bridge that is to span a river 20 meters wide. The center of the arch is 6 meters above the center of the
river. See the figure. Write an equation for the ellipse in which thex- axis coincides with the waterlevel
and they- axis passes through the center of the arch.
6. Whispering Gallery: A hall 100 feet in length is to be designed as a whispering gallery. If the foci are
located 25 feet from the center, how high will the ceiling be at the center? Round your answer to the
nearest hundredth.
Unit 2: Conics HOMEWORK
Introduction to Analysis Honors
Lesson 4 - Hyperbolas Day 1
Find an equation for the hyperbola described:
1. Center at(0, 0)
Focus at(3, 0)
Vertex at(1, 0)
3. Vertices at(0, ± 6)
Asymptote at the line𝑦 = 2𝑥
2. Center at(0, 0)
Focus at(0, − 6)
Vertex at(0, 4)
nalyze each equation: find the center, vertices, co-vertices, transverse axis, foci and asymptotes. Graph
A
each equation by hand.
4.
2
2
𝑥
𝑦
− 9
25
2
2
= 1
= 9
5.𝑦 − 9𝑥
5. Write the equation for the hyperbola in the given picture.
Unit 2: Conics HOMEWORK
Introduction to Analysis Honors
Lesson 5 - Hyperbolas Day 2
Find an equation for the hyperbola described:
1. Center at(4, − 1)
Focus at(7, − 1)
Vertex at(6, − 1)
3. Foci at(3, 7) &(7, 7)
Vertex at(6, 7)
2. Center at(− 3, − 4)
Focus at(− 3, − 8)
Vertex at(− 3, − 2)
Graph the equation of each hyperbola.
4.
2
(𝑥−2)
4
−
2
2
(𝑦+
3)
9
2
= 1
− 4𝑦
− 8𝑥
− 4 = 0
5. 𝑦 − 4𝑥
2
2
6. 4𝑥
− 𝑦 − 24𝑥 − 4𝑦
+ 16 = 0
0
