NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Chapter 7 Test, Form 2A
SCORE ______________
Write the letter for the correct answer in the blank at the right of each question.
For Questions 1–3, refer to the ellipse represented by the equation
(𝒙 − 𝟑)𝟐
𝟐𝟓
+ (𝒚 − 𝟐)𝟐 = 1.
1. Find the coordinates of the center.
A (2, 3)
B (3, 2)
C (–3, –2)
D (–2, –3)
B
1. _______________
2. Find the coordinates of the foci.
F (3, 2 ± 2√6 )
G (–2, 2) , (8, 2)
H ( 3 ± 2√6 , 2)
J ( 2 ± 2√6 , 3)
2. _______________
H
3. Find the coordinates of the vertices and co-vertices.
A (8, 2) , (–2, 2) , (3, 3) , (3, 1)
C (4, 2) , (2, 2) , (3, 3) , (3, 1)
B (8, 2) , (–2, 2) , (3, 7) , (3 , –3)
D (4, 2) , (2, 2) , (3, 7) , (3, –3)
A
3. _______________
4. Determine the angle of rotation θ through which the conic given by equation
2𝑥 2 + 3xy + 𝑦 2 = 1 should be rotated.
F –9˚
G 36˚
H –36˚
J 324˚
G
4. _______________
5. Write the pair of parametric equations x = 3 cos θ and y = sin θ in rectangular form.
A
𝑥2
9
+ 𝑦2 = 1
B
𝑥2
9
– 𝑦2 = 1
C 𝑦2 –
𝑥2
3
=1
D 𝑦2 +
𝑥2
3
=1
A
5. _______________
6. Use the discriminant to identify the conic section 3𝑦 2 – 3𝑥 2 + 12y + 18x = 42.
F parabola
G hyperbola
H ellipse
J circle
G
6. _______________
7. Write the standard form of the equation 𝑦 2 – 𝑥 2 = 2 in the x′y′ plane after a rotation of 45˚.
A x′y′ = 1
B x′y′ = –2
C ( 𝑦′)2 – (𝑥′)2 = 2
D (𝑥′)2 = y′
A
7. _______________
8. Randall hit a golf ball with an initial velocity of 120 feet per second at an angle of 38˚ with
the ground. Write parametric equations to represent this situation.
F x = 120t cos 38˚ – 16𝑡 2
H x = 38t cos 120˚
y = 120t sin 38˚
y = 38t sin 120˚ – 16𝑡 2
G x = 120t cos 38˚
J x = 38 cos 120t˚
y = 120t sin 38˚ – 16𝑡 2
y = 38 cos 120t˚
8. _______________
9. A cross section of the reflector shown is in the shape
of a parabola. Write an equation for the cross section.
A 𝑦 2 = 4x
C 𝑥 2 = 4y
B 𝑦 2 = 8x
D 𝑥 2 = 8y
9. _______________
B
Chapter 7
39
G
Glencoe Precalculus
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Chapter 7 Test, Form 2A
(continued)
For Questions 10 and 11, refer to the hyperbola represented by
(𝒚 + 𝟐)𝟐
𝟑𝟔
10. Write the equations of the asymptotes.
F y – 1 = ± 6 (x – 2)
G y = ± 6x
H y + 2 = ± 6 (x – 1)
J y + 2 = ± 6x
11. Find the coordinates of the foci.
A (1 ± √37, –2)
B (± √37, –2)
C (6 ± √37, –2)
– 𝒙𝟐 = 1.
J
10. _______________
D (0, –2 ± √37 )
11. _______________
D
12. Write the standard form of the equation of the hyperbola for which a = 2, the transverse
axis is vertical, and the equations of the asymptotes are y = ± 2x.
F
𝑥2
4
– 𝑦2 = 1
G 𝑦2 –
𝑥2
4
=1
H 𝑥2 –
𝑦2
4
=1
J
𝑦2
4
– 𝑥2 = 1
J
12. _______________
13. Aaron kicked a soccer ball with an initial velocity of 39 feet per second at an angle of 44˚
with the horizontal. After 0.9 second, how far has the ball traveled horizontally?
A 24.4 ft
B 12.3 ft
C 11.4 ft
D 25.2 ft
13. _______________
14. Write the standard form of the equation of the parabola with directrix at y = –4 and
focus at (2, 2) .
F (𝑦 − 2)2 = 12 (x + 2)
H (𝑥 + 2)2 = 12 (y – 2)
2
G y + 1 = 12 (𝑥 − 2)
J (𝑥 − 2)2 = 12 (y + 1)
J
14. _______________
15. Identify the graph of the equation 4𝑥 2 – 5xy + 16𝑦 2 – 32 = 0.
A circle
B ellipse
C parabola
B
15. _______________
D hyperbola
16. Which graph represents a curve given by x = 4t + 5 and y = 2𝑡 2 over the interval
–3 ≤ t ≤ 3?
F
G
H
J
D
F
16. _______________
2
17. Identify the conic that has an eccentricity of 3.
A circle
B ellipse
C hyperbola
D parabola
18. Write the standard form of the equation of the circle with center at (–3, 5) that is tangent
to the y-axis.
F (𝑥 + 3)2 + (𝑦 − 5)2 = 9
H (𝑥 + 3)2 + (𝑦 − 5)2 = 3
2
2
G (𝑥 + 3) + (𝑦 − 5) = 25
J (𝑥 − 3)2 + (𝑦 + 5)2 = 9
B
17. _______________
F
18. _______________
𝟏
2
Bonus Write the equation of the line tangent to (𝑦 − 2) = 8x at (8, –6).
Chapter 7
40
y = – 𝟐x – 2
B: _______________
Glencoe Precalculus