# Honors Algebra 2: Assignment 74 Unit Review

• Class: Honors Algebra 2
• Author: Peter Atlas
• Text: Algebra and Trigonometry: Structure and Method, Brown

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1. Write the equation for the parabola with focus $$(3, 2)$$ and directrix $$y = -1.$$
2. Solution

$$\displaystyle y = \frac{1}{6}\left(x - 3\right)^2 + \frac{1}{2}$$

3. Graph $$x = 5(y + 3)^2 + 7.$$ Give the coordinates of the vertex and the equation of the axis of symmetry.
4. Solution

A parabola opening right. Vertex at $$(7, -3),$$ axis of symmetry $$y = -3.$$

5. Find the equation of a parabola determined by vertex $$(0, 0)$$ and focus $$(3, 0).$$
6. Solution

$$\displaystyle x = \frac{1}{12}y^2$$

7. Find an equation of the ellipse with $$\displaystyle \left(0, \pm \sqrt{3}\right)$$as foci and 4 as the sum of the focal radii.
8. Solution

$$\displaystyle x^2 + \frac{y^2}{4} = 1$$

9. Graph $$9x^2 + 49y^2 = 441.$$ Give the x- and y-intercepts. Find the coordinates of the foci.
10. Solution

A horizontal ellipse centered at the origin with x-intercepts $$( \pm 7, 0)$$ and y-intercepts $$(0, \pm3).$$ The foci are $$\displaystyle \left( \pm 2\sqrt{10}, 0\right).$$

11. Sketch the graph and label the coordinates of the foci and vertices:$$9x^2 - 4y^2 - 18x + 16y - 43 = 0.$$
12. Solution

A horizontal hyperbola with center $$(1, 2),$$ vertices $$(-1, 2)$$ and $$(3, 2),$$ and foci $$(1 \pm \sqrt{13}, 2)$$

13. Sketch the graph and label the coordinates of the foci and vertices: $$y^2 - 9x^2 - 36x - 45 = 0.$$
14. Solution

A vertical hyperbola with center $$(-2, 0),$$ vertices $$(-2, \pm 3),$$ and foci $$(-2, \pm \sqrt{10}).$$

15. Find an equation of the hyperbola with foci at $$(\pm 5, 0)$$ and asymptotes $$\displaystyle y = \pm \frac{2}{3}x.$$
16. Solution

$$\displaystyle \frac{x^2}{\frac{225}{13}} - \frac{y^2}{\frac{100}{13}} = 1.$$

17. Determine an equation of the form $$x^2 + y^2 + ax + by + c = 0$$ for the circle with center $$(-1, 5)$$ and passing through the point $$(-1, 8).$$
18. Solution

$$x^2 + y^2 + 2x - 10y + 17 = 0.$$

19. Sketch the graph of the inequality $$x^2 + y^2 > 6x.$$
20. Solution

This is a dotted circle with center $$(3, 0)$$ and radius 3 shaded outside.

21. Identify the following as circle, parabola, ellipse, or hyperbola: $$x^2 + y^2 - 8x + 2y = -8.$$
22. Solution

circle

23. Identify the following as circle, parabola, ellipse, or hyperbola: $$x^2 = 8y.$$
24. Solution

parabola

25. Identify the following as circle, parabola, ellipse, or hyperbola: $$36x^2 - 4y^2 - 144 = 0.$$
26. Solution

hyperbola

27. Identify the following as circle, parabola, ellipse, or hyperbola: $$x^2 + 4y^2 - 16 = 0.$$
28. Solution

ellipse

29. Identify the following as circle, parabola, ellipse, or hyperbola: $$x + 2y^2 - 8y + 4 = 0.$$
30. Solution

parabola