Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Mathematics LibreTexts

10.8.2: Practice Test

( \newcommand{\kernel}{\mathrm{null}\,}\)

Practice Test

For the following exercises, write the equation in standard form and state the center, vertices, and foci.

1.

𝑥29+𝑦24=1

2.

9𝑦2+16𝑥236𝑦+32𝑥92=0

For the following exercises, sketch the graph, identifying the center, vertices, and foci.

3.

(𝑥3)264+(𝑦2)236=1

4.

2𝑥2+𝑦2+8𝑥6𝑦7=0

5.

Write the standard form equation of an ellipse with a center at (1,2), vertex at (7,2), and focus at (4,2).

6.

A whispering gallery is to be constructed with a length of 150 feet. If the foci are to be located 20 feet away from the wall, how high should the ceiling be?

For the following exercises, write the equation of the hyperbola in standard form, and give the center, vertices, foci, and asymptotes.

7.

𝑥249𝑦281=1

8.

16𝑦29𝑥2+128𝑦+112=0

For the following exercises, graph the hyperbola, noting its center, vertices, and foci. State the equations of the asymptotes.

9.

(𝑥3)225(𝑦+3)21=1

10.

𝑦2𝑥2+4𝑦4𝑥18=0

11.

Write the standard form equation of a hyperbola with foci at (1,0) and (1,6), and a vertex at (1,2).

For the following exercises, write the equation of the parabola in standard form, and give the vertex, focus, and equation of the directrix.

12.

𝑦2+10𝑥=0

13.

3𝑥212𝑥𝑦+11=0

For the following exercises, graph the parabola, labeling the vertex, focus, and directrix.

14.

(𝑥1)2=4(𝑦+3)

15.

𝑦2+8𝑥8𝑦+40=0

16.

Write the equation of a parabola with a focus at (2,3) and directrix 𝑦=1.

17.

A searchlight is shaped like a paraboloid of revolution. If the light source is located 1.5 feet from the base along the axis of symmetry, and the depth of the searchlight is 3 feet, what should the width of the opening be?

For the following exercises, determine which conic section is represented by the given equation, and then determine the angle 𝜃 that will eliminate the 𝑥𝑦 term.

18.

3𝑥22𝑥𝑦+3𝑦2=4

19.

𝑥2+4𝑥𝑦+4𝑦2+6𝑥8𝑦=0

For the following exercises, rewrite in the 𝑥𝑦 system without the 𝑥𝑦 term, and graph the rotated graph.

20.

11𝑥2+103𝑥𝑦+𝑦2=4

21.

16𝑥2+24𝑥𝑦+9𝑦2125𝑥=0

For the following exercises, identify the conic with focus at the origin, and then give the directrix and eccentricity.

22.

𝑟=32sin𝜃

23.

𝑟=54+6cos𝜃

For the following exercises, graph the given conic section. If it is a parabola, label vertex, focus, and directrix. If it is an ellipse or a hyperbola, label vertices and foci.

24.

𝑟=1248sin𝜃

25.

𝑟=24+4sin𝜃

26.

Find a polar equation of the conic with focus at the origin, eccentricity of 𝑒=2, and directrix: 𝑥=3.


10.8.2: Practice Test is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

  • Was this article helpful?

Support Center

How can we help?