Find the vertex, focus, and directrix of the parabola, and

Find the vertex, focus, and directrix of the parabola, and sketch the graph.y 2 4x

Find the vertex, focus, and directrix of the parabola, and sketch the graph.x 1 12 y2

Find the vertex, focus, and directrix of the parabola, and sketch the graph.x 2 8y 0 4

Find the vertex, focus, and directrix of the parabola, and sketch the graph.2x  y 2 0

Find the vertex, focus, and directrix of the parabola, and sketch the graph.x  y 2 4y  2 0 6

Find the vertex, focus, and directrix of the parabola, and sketch the graph.2x 2 6x 5y 10 0 7.

Find the vertex, focus, and directrix of the parabola, and sketch the graph. 2 x 2 2x 2y 4 x

Find the vertex, focus, and directrix of the parabola, and sketch the graph.x 2 31x y2 1

Find the center, vertices, foci, and the lengths of the major and minor axes of the ellipse, and sketch the graph.x 2 9 y2 25 1 x

Find the center, vertices, foci, and the lengths of the major and minor axes of the ellipse, and sketch the graph.x 2 49 y2 9 1 x

Find the center, vertices, foci, and the lengths of the major and minor axes of the ellipse, and sketch the graph.x 2 4y 2 16 1

Find the center, vertices, foci, and the lengths of the major and minor axes of the ellipse, and sketch the graph.9x 2 4y 2 1

Find the center, vertices, foci, and the lengths of the major and minor axes of the ellipse, and sketch the graph.1x  32 2 9 y2 16 1

Find the center, vertices, foci, and the lengths of the major and minor axes of the ellipse, and sketch the graph.1x  22 2 25 1y 32 2 16 1 1x

Find the center, vertices, foci, and the lengths of the major and minor axes of the ellipse, and sketch the graph.4x 2 9y 2 36y 1

Find the center, vertices, foci, and the lengths of the major and minor axes of the ellipse, and sketch the graph.2x 2 y2 2 41x  y2 1

Find the center, vertices, foci, and asymptotes of the hyperbola, and sketch the graph.x 2 9 y2 16 1

Find the center, vertices, foci, and asymptotes of the hyperbola, and sketch the graph.x 2 49  y2 32  1 x

Find the center, vertices, foci, and asymptotes of the hyperbola, and sketch the graph.x 2  2y 2 16

Find the center, vertices, foci, and asymptotes of the hyperbola, and sketch the graph.x 2  4y 2 16 0\

Find the center, vertices, foci, and asymptotes of the hyperbola, and sketch the graph.1x 42 2 16  y2 16 1

Find the center, vertices, foci, and asymptotes of the hyperbola, and sketch the graph.1x  22 2 8  1y 22 2 8 1

Find the center, vertices, foci, and asymptotes of the hyperbola, and sketch the graph.9y 2 18y x 2 6x 18 24.

Find the center, vertices, foci, and asymptotes of the hyperbola, and sketch the graph.y 2 x 2 6y

Find an equation for the conic whose graph is shown.x y 2 F(2, 0)

Find an equation for the conic whose graph is shown.x y 5 _12 _5

Find an equation for the conic whose graph is shown.x y 4 F(0, 5

Find an equation for the conic whose graph is shown.x y V(4, 4) 4 8

Find an equation for the conic whose graph is shown.x 2 y 2

Find an equation for the conic whose graph is shown.x y 1

Determine the type of curve represented by the equation. Find the foci and vertices (if any), and sketch the graph.x 2 12 y 1

Determine the type of curve represented by the equation. Find the foci and vertices (if any), and sketch the graph.x 2 12 y2 144 y 12

Determine the type of curve represented by the equation. Find the foci and vertices (if any), and sketch the graph.x 2  y 2 144 0

Determine the type of curve represented by the equation. Find the foci and vertices (if any), and sketch the graph.x 2 6x 9y 2

Determine the type of curve represented by the equation. Find the foci and vertices (if any), and sketch the graph.4x 2 y2 81x y2 x

Determine the type of curve represented by the equation. Find the foci and vertices (if any), and sketch the graph.3x 2  61x y2 10

Determine the type of curve represented by the equation. Find the foci and vertices (if any), and sketch the graph.x y 2  16y

Determine the type of curve represented by the equation. Find the foci and vertices (if any), and sketch the graph.2x 2 4 4x y 2 3

Determine the type of curve represented by the equation. Find the foci and vertices (if any), and sketch the graph.2x 2  12x y 2 6y 26 0 40

Determine the type of curve represented by the equation. Find the foci and vertices (if any), and sketch the graph.36x 2  4y 2  36x  8y 31

Determine the type of curve represented by the equation. Find the foci and vertices (if any), and sketch the graph.9x 2 8y 2  15x 8y 27 0 42

Determine the type of curve represented by the equation. Find the foci and vertices (if any), and sketch the graph.x 2 4y 2 4x 8 4

Find an equation for the conic section with the given properties.The parabola with focus and directrix y 1

Find an equation for the conic section with the given properties.The ellipse with center , foci and , and major axis of length 10

Find an equation for the conic section with the given properties.

Find an equation for the conic section with the given properties.The hyperbola with center C12, 42 foci F 12, 12 and , 22 112, 62 F

Find an equation for the conic section with the given properties.The ellipse with foci and , and with one vertex on the x-axis

Find an equation for the conic section with the given properties.The parabola with vertex V15, 52 and directrix the y-axis

Find an equation for the conic section with the given properties.The ellipse with vertices and , and passing through the point

Find an equation for the conic section with the given properties.The parabola with vertex and horizontal axis of symmetry, and crossing the y-axis at y 2

The path of the earth around the sun is an ellipse with the sun at one focus. The ellipse has major axis 186,000,000 mi and eccentricity 0.017. Find the distance between the earth and the sun when the earth is (a) closest to the sun and (b) farthest from the sun

A ship is located 40 mi from a straight shoreline. LORAN stations A and B are located on the shoreline, 300 mi apart. From the LORAN signals, the captain determines that his ship is 80 mi closer to A than to B. Find the location of the ship. (Place A and B on the y-axis with the x-axis halfway between them. Find the x- and y-coordinates of the ship.)

(a) Draw graphs of the following family of ellipses for k 1, 2, 4, and 8. (b) Prove that all the ellipses in part (a) have the same foci.

(a) Draw graphs of the following family of parabolas for , 1, 2, and 4. (b) Find the foci of the parabolas in part (a). (c) How does the location of the focus change as k increases?

An equation of a conic is given. (a) Use the discriminant to determine whether the graph of the equation is a parabola, an ellipse, or a hyperbola. (b) Use a rotation of axes to eliminate the xy-term. (c) Sketch the graph.x 2 4xy y 2 1 5

An equation of a conic is given. (a) Use the discriminant to determine whether the graph of the equation is a parabola, an ellipse, or a hyperbola. (b) Use a rotation of axes to eliminate the xy-term. (c) Sketch the graph.5x 2  6xy 5y 2  8x 8y  8 0 5

An equation of a conic is given. (a) Use the discriminant to determine whether the graph of the equation is a parabola, an ellipse, or a hyperbola. (b) Use a rotation of axes to eliminate the xy-term. (c) Sketch the graph.7x 2  6 13xy 13y2  4 13x  4y 0

An equation of a conic is given. (a) Use the discriminant to determine whether the graph of the equation is a parabola, an ellipse, or a hyperbola. (b) Use a rotation of axes to eliminate the xy-term. (c) Sketch the graph.9x 2 24xy 16y 2 25 5

Use a graphing device to graph the conic. Identify the type of conic from the graph.5x 2 3y 2 60 6

Use a graphing device to graph the conic. Identify the type of conic from the graph.9x 2  12y 2 36 0

Use a graphing device to graph the conic. Identify the type of conic from the graph.6x y 2  12y 30 6

Use a graphing device to graph the conic. Identify the type of conic from the graph.52x 2  72xy 73y 2 100

A polar equation of a conic is given. (a) Find the eccentricity and identify the conic. (b) Sketch the conic and label the vertices.r 1 1  cos u

A polar equation of a conic is given. (a) Find the eccentricity and identify the conic. (b) Sketch the conic and label the vertices.r 2 3 2 sin u r

A polar equation of a conic is given. (a) Find the eccentricity and identify the conic. (b) Sketch the conic and label the vertices.r 4 1 2 sin u

A polar equation of a conic is given. (a) Find the eccentricity and identify the conic. (b) Sketch the conic and label the vertices.r 12 1  4 cos u