ALGEBRA II/TRIG – CONIC WORKSHEET #3 Identify the following conics, complete the square and state pertinent information, such as center, vertices, radius, endpoints of axes, axes of symmetry, equations of asymptotes, etc. 1. x2 – 6x + y2 – 4y – 12 = 0 3. 9x2 – 16y2 – 54x + 64y – 127 = 0 2. 9x2 + 25y2 – 54x – 100y – 44 = 0 4. 49x2 + 196x + 4y2 – 40y + 100 = 0 Given the following parabolas, put into center/vertex form by completing the square, state the vertex, how it opens, and if it has a scale change. 5. x2 + 6x + 4y + 8 = 0 7. 4y2 = 8y + 2x

6. y2 + 6x + 10y + 19 = 0 Find the equations of the following conics. 8. A parabola with vertex at (-4,2), axis of symmetry at y = 2, going through (0,6). 9. A hyperbola with center at (1,3), one vertex at (4,3) , and 2b = 4. 10. A hyperbola with vertices at (3,-1) and (3,5), and the equations of the asymptotes are x – y

= 1 and x + y = 5. 11. A hyperbola with vertices at (0,0) and (12,0), and the equations of the asymptotes are 4x –

3y = 24 and 4x + 3y = 24.

12. An ellipse with center at (5,1), and the points (3,1) and (5,6) are endpoints of axes. 13. An ellipse with (-1,3) and (5,3) as the endpoints of one of its axes, and the length of its minor

axis is 4. 14. An ellipse with the ends of its minor axis at (4,2) and (4,-6) and one endpoint of the major

axis at (9,-2).