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Algebra 2 – Unit 11
11 Corrective Assignment – Conic Sections
Unit 11
Equations
(𝒙 − 𝒉)
𝟐
= 𝟒𝒑(𝒚 − 𝒌)
or
(𝒚 − 𝒌)
𝟐
= 𝟒𝒑(𝒙 − 𝒉)
( 𝒙 − 𝒉
)
𝟐
𝒃
𝟐
( 𝒚 − 𝒌
)
𝟐
𝒂
𝟐
= 𝟏
or
(𝒙 − 𝒉)
𝟐
𝒂
𝟐
(𝒚 − 𝒌)
𝟐
𝒃
𝟐
= 𝟏
( 𝒚 − 𝒌
)
𝟐
𝒂
𝟐
−
( 𝒙 − 𝒉
)
𝟐
𝒃
𝟐
= 𝟏
or
(𝒙 − 𝒉)
𝟐
𝒂
𝟐
−
(𝒚 − 𝒌)
𝟐
𝒃
𝟐
= 𝟏
(𝒙 − 𝒉)
𝟐
𝟐
= 𝒓
𝟐
𝒙
𝟐
𝒃
𝟐
)
𝟐
= (𝒙 +
𝒃
𝟐
)
𝟐
- Sketch the graph of
2
and identify the given
information.
Coordinate of vertex:
Direction it opens:
Coordinate of focus:
Equation of directrix:
For 2-3, given the following conditions, find an equation for the parabola. Use the conics form with the
quantity squared isolated.
- Vertex:
Directrix: 𝑦 = − 4. 3. Focus:
Directrix: 𝑥 = − 1
- Sketch the graph of 𝑥
2
2
= 36 and identify the
coordinate points for each of the following.
Center:
Vertices:
Co-vertices:
Foci:
- Write the equation of a circle with
a center at ( 2 , 13 ) and radius of 3.
- Sketch the graph of
2
2
- Write the standard form
equation of the circle.
For 8 - 9 , given the following conditions, write the standard form
equation of the ellipse.
For 1 0 - 11 , write the standard form
equation of the hyperbola.
- Vertices:
Co-vertices
A)
(𝑥− 8 )
2
36
(𝑦− 5 )
2
25
B)
(𝑥+ 8 )
2
36
(𝑦+ 5 )
2
25
C)
( 𝑥+ 8
)
2
25
( 𝑦+ 5
)
2
36
D)
( 𝑥− 8
)
2
25
( 𝑦− 5
)
2
36
- Vertices:
Foci:
A)
(𝑥− 9 )
2
169
(𝑦− 5 )
2
144
B)
(𝑥+ 9 )
2
144
(𝑦− 5 )
2
169
C)
( 𝑥+ 8
)
2
144
( 𝑦+ 7
)
2
169
D)
( 𝑥− 9
)
2
144
( 𝑦− 5
)
2
169
- Vertices:
Endpoints of Conjugate Axis:
A)
(𝑥+ 6 )
2
9
(𝑦− 1 )
2
144
B)
( 𝑦− 1
)
2
144
( 𝑥+ 6
)
2
9
C)
( 𝑥+ 6
)
2
144
( 𝑦− 1
)
2
9
D)
(𝑦− 1 )
2
9
(𝑥+ 6 )
2
144
x
y
- A radio station has a broadcast radius of 63 miles.
a. Write an inequality that represents the broadcast range of the station. (Assume the center is at
the origin.)
b. Your house is located 51 miles east and 37 miles north of the radio station. Is your house within
the broadcast range? (Plug in these values to your inequality.)
ANSWERS to Unit 11 Corrective Assignment
Vertex: ( 2 , − 2 )
Direction: right
Focus: ( 5 , − 2 )
Directrix: 𝑥 = − 1
𝑥
2
= 24 (𝑦 − 2 )
Center: ( 0 , − 1 )
Vertices: (− 6 , − 1 )
( 6 , − 1 )
Co-vertices: ( 0 , − 2 )
( 0 , 0 )
Foci: (±√ 35 , − 1 )
(𝑥 − 2 )
2
2
= 9
(𝑦 + 8 )
2
= 12 (𝑥 − 2 )
(𝑥 − 4 )
2
2
= 25
D)
(𝑥− 8 )
2
25
(𝑦− 5 )
2
36
A)
(𝑥− 9 )
2
169
(𝑦− 5 )
2
144
C)
( 𝑥+ 6
)
2
144
( 𝑦− 1
)
2
9
D)
(𝑥+ 3 )
2
4
−
( 𝑦 + 2
)
2
= 1
(𝑦 + 5 )
2
= −
1
3
(𝑥 + 2 )
Parabola
(𝑥 − 2 )
2
2
= 2
Circle
- 5 inches 15.
𝑥
2
100
𝑦
2
16
= 1
16 a.
𝑥
2
2
= 1296
16 b.
𝑥 ≈ 18. 3
Width = 36. 6 inches
17 a.
𝑥
2
2
≤ 3969
17 b.
3970 ≤ 3969 (FALSE)
No! It is not within range
x
y
