Precalculus by Richard Wright

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Better a little with righteousness than much gain with injustice. Proverbs 16:8 NIV

7-Review

Take this test as you would take a test in class. When you are finished, check your work against the answers. On this assignment round your answers to three decimal places unless otherwise directed.

  1. Find the inclination of 2x + y − 3 = 0 in degrees.
  2. Find the angle between the lines 2x + y − 3 = 0 and x − 2y + 1 = 0.
  3. Find the distance between (2, 4) and 2x + y − 3 = 0.
  4. Classify the conic 4x2 + 9y2 − 8x + 36y + 4 = 0.
  5. Find the foci of 4x2 + 9y2 − 8x + 36y + 4 = 0.
  6. Graph 4x2 + 9y2 − 8x + 36y + 4 = 0.
  7. Find the standard form of the equation of the parabola with focus (3, 0) and directrix x = −1.
  8. Find the standard form of the hyperbola with vertices (2, 5) and (−4, 5) and b = 5.
  9. Classify the conic x2 − 2xy + 2y2 + 3x − 5y + 12 = 0.
  10. What degree is x2 − 2xy + 2y2 + 3x − 5y + 12 = 0 rotated?
  11. Graph the parametric equations \(x = \sqrt{t}\) and y = 2t2.
  12. Eliminate the parameter from \(x = \sqrt{t}\) and y = 2t2.
  13. Convert \(\left(4, \frac{π}{3}\right)\) to rectangular coordinates.
  14. Find another polar coordinate that represents \(\left(4, \frac{π}{3}\right)\).
  15. Convert r = 4 sec θ to rectangular form.
  16. Graph the polar coordinate \(\left(2, \frac{7π}{6}\right)\).
  17. Classify the graph of \(r = \frac{6}{1 - 3 \cos θ}\).
  18. Find one focus of \(r = \frac{6}{1 - 3 \cos θ}\).
  19. Classify the graph of \(r = \frac{3}{1 + \sin θ}\).
  20. Find the polar equation for an ellipse with directrix x = −6 and \(e = \frac{1}{3}\).
  21. Find the polar equation for a hyperbola with the vertices \(\left(2, \frac{π}{2}\right)\) and \(\left(-6, \frac{3π}{2}\right)\).

Answers

  1. 116.6°
  2. 90°
  3. \(\sqrt{5}\)
  4. Ellipse
  5. \(\left(1 ± \sqrt{5}, -2\right)\)
  6. ans
  7. y2 = 8(x − 1)
  8. \(\frac{\left(x + 1\right)^2}{9} - \frac{\left(y - 5\right)^2}{25} = 1\)
  9. Ellipse
  10. 31.7°
  11. ans
  12. y = 2x4
  13. \(\left(2, 2\sqrt{3}\right)\)
  14. \(\left(4, \frac{7π}{3}\right)\) or \(\left(-4, \frac{4π}{3}\right)\)
  15. x = 4
  16. ans
  17. Hyperbola with vertical directrix to the left of the pole
  18. (0, 0)
  19. Parabola with horizontal directrix above the pole
  20. \(r = \frac{6}{3 - \cos θ}\)
  21. \(r = \frac{6}{1 + 2 \sin θ}\)