Precalculus by Richard Wright

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

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.

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

- 116.6°
- 90°
- \(\sqrt{5}\)
- Ellipse
- \(\left(1 ± \sqrt{5}, -2\right)\)
- \(y^2 = 8\left(x - 1\right)\)
- \(\frac{\left(x + 1\right)^2}{9} - \frac{\left(y - 5\right)^2}{25} = 1\)
- Ellipse
- 31.7°
- \(y = 2x^4\)
- \(\left(2, 2\sqrt{3}\right)\)
- \(\left(4, \frac{7π}{3}\right)\) or \(\left(-4, \frac{4π}{3}\right)\)
- \(x = 4\)
- Hyperbola with vertical directrix to the left of the pole
- (0, 0)
- Parabola with horizontal directrix above the pole
- \(r = \frac{6}{3 - \cos θ}\)
- \(r = \frac{6}{1 + 2 \sin θ}\)