Precalculus Test 4 Practice Questions Page 1 of 7 Note: You can expect other types of questions on the test than the ones presented here! Questions Example 1 Eliminate the parameter and sketch the parametric curve given by x = t - 2, y =3/t, |t| < 1. Example 2 Solve the system of equations x 2 + y 2 = 9 and x 2 - y = 2. Sketch the situation to check that you found the correct number of solutions. Example 3 Sketch the region defined by x 2 - 2x + y 2 ≥ 8 and y> |x +1|. Example 4 A parabola is the set of all points in a plane equidistant from a particular line (the directrix) and a particular point (the focus) in the plane. If the focus is (0,p) and the directrix is y = -p, derive the equation of the parabola x 2 =4yp. Include a well labeled sketch of the situation to motivate your calculations. Example 5 Sketch 4x 2 + y 2 - 32x + 16y + 124 = 0. Locate the center, vertices, and foci of the ellipse. Example 6 Sketch 9x 2 - 54x - 4y 2 +8y + 113 = 0. Locate the vertices and foci of the hyperbola.
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Precalculus Test 4 Practice Questions Page 1 of 7
Note: You can expect other types of questions on the test than the ones presented here!
Questions
Example 1 Eliminate the parameter and sketch the parametric curve given by x = t− 2, y = 3/t, |t| < 1.
Example 2 Solve the system of equations x2 + y2 = 9 and x2 − y = 2. Sketch the situation to check that you found thecorrect number of solutions.
Example 3 Sketch the region defined by x2 − 2x + y2 ≥ 8 and y > |x + 1|.
Example 4 A parabola is the set of all points in a plane equidistant from a particular line (the directrix) and a particularpoint (the focus) in the plane. If the focus is (0, p) and the directrix is y = −p, derive the equation of the parabola x2 = 4yp.Include a well labeled sketch of the situation to motivate your calculations.
Example 5 Sketch 4x2 + y2 − 32x + 16y + 124 = 0. Locate the center, vertices, and foci of the ellipse.
Example 6 Sketch 9x2 − 54x− 4y2 + 8y + 113 = 0. Locate the vertices and foci of the hyperbola.
Precalculus Test 4 Practice Questions Page 2 of 7
Solutions
Precalculus Test 4 Practice Questions Page 3 of 7
Precalculus Test 4 Practice Questions Page 4 of 7
Precalculus Test 4 Practice Questions Page 5 of 7
Precalculus Test 4 Practice Questions Page 6 of 7
Precalculus Test 4 Practice Questions Page 7 of 7
Related Documents
![4452 Mathematical Modeling Lecture 13: Chaos and …cda.mrs.umn.edu/.../teachingarchive/M4452/Lecture13.pdfChaos and Fractals: New Frontiers of Science [1] which clocks in at over](https://static.cupdf.com/doc/110x72/5f6ff1c4272cf652576b8874/4452-mathematical-modeling-lecture-13-chaos-and-cdamrsumneduteachingarchivem4452.jpg)
