Write each equation in standard form (or vertex form if it’s a parabola). State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. State the center or vertex of the conic section. If it is an ellipse or hyperbola, state the direction of the major/transverse axis.

1. 2.

3. 4.

5. Write the equation in vertex form. State the vertex, focus, and equation of the directrix. Make sure to show the directrix, focus, and vertex on the graph, as well as at least two other ordered pairs.

Vertex form: ______

Vertex: ______

Focus: ______

Directrix: ______; LLR: ______

1. Find the equation of the circle given the following information. Then graph the circle. State the center and the radius of the circle.

The endpoints of the diameter at (6, 6) and (10, 12)

Center: ______

Equation: ______

1. Find the coordinates of the center, foci, and the lengths of the major and minor axes for the ellipse with the given equation. Then graph the ellipse.

Center: ______

Length of major axis: ______

Length of minor axis: ______

Foci: ______

8. Find the coordinates of the center and vertices for the given equation. Then graph the hyperbola (draw ALL parts including the rectangle and asymptotes).

Center: ______

Vertices: ______

Length of Transverse Axis: ______

Length of Conjugate Axis: ______

Foci: ______

Equation of the Asymptotes: ______

9.Write the equation of a circle in standard form with center (1, 0) that contains the

point (–3, 2)

Find an equation for the parabola described. You do not have to graph the parabola – the graph is to help you sketch and visualize the parabola.

10. Vertex at (–1, –2); focus at (0, –2)11. Focus at (–3, 4); directrix is y = 2.

Write an equation in standard form for the ellipse described. You do not have to graph the ellipse – the graph is to help you sketch and visualize the ellipse.

12. Foci (1, 2) and (–3, 2); vertex (–4, 2).13. Foci (–3, 5) and (–3, –7); length of major axis is 14.

Write an equation in standard form for the hyperbola described. You do not have to graph the hyperbola – the graph is to help you sketch and visualize the hyperbola.

14.center at (–3, –4); focus at (–3, –8); vertex at (–3, –2)

Find the vertex form, vertex, focus, directrix, and LLR of the parabola. Graph the equation.

15.

Vertex Form:

Vertex: ______

Focus: ______

Directrix:______

LLR: ______

Just enough so you know whether or not you are on the right track!! To see complete solutions, please go to my website and click on the “KEY Review – Conics Unit” on the course calendar.

1. Hyperbola ~ standard form: ; transverse axis vertical; center (0, 0)

2. Circle ~ standard form: ; center (–1, –3); radius: 6

3. Parabola ~ vertex form: ; vertex: (–8, –6)

4. Ellipse ~ standard form: ; major axis horizontal; center (0, 1)

5. Vertex form: ; vertex: (12, 3); opens to the left

6. Circle center: (8, 9); Radius =

7. Ellipse center: (–4, –3); major axislength = 14, minor axis length = 10

8. Hyperbola center: (0, 0); Vertices: (2, 0) and (–2, 0)

9.

10.

11.

12.

13.

14.

15. Vertex form: ; vertex: (2, –1); opens to the left