Solved: Show that the graph of an equation of the form Cy2

The formula for the distance d from P1 = 1x1 , y12 to P2 = 1x2 , y22 is d = _____. (p. 5)

To complete the square of x2 - 4x, add . (pp. A28A29)

Use the Square Root Method to find the real solutions of 1x + 422 = 9. (p. A47)

The point that is symmetric with respect to the x-axis to the point 1 -2, 52 is ________. (pp. 1920)

To graph y = 1x - 322 + 1, shift the graph of y = x2 to the right units and then 1 unit. (pp. 104106)

A(n) is the collection of all points in the plane such that the distance from each point to a fixed point equals its distance to a fixed line

If a 7 0, the equation of the parabola is of the form (a) 1y - k22 = 4a1x - h2 (b) 1y - k22 = -4a1x - h2 (c) 1x - h22 = 4a1y - k2 (d) 1x - h22 = -4a1y - k2

The coordinates of the vertex are .

If a = 4, then the coordinates of the focus are .

If a = 4, then the equation of the directrix is .

In Problems 1118, the graph of a parabola is given. Match each graph to its equation. (A) y2 = 4x (B) x2 = 4y (C) y2 = -4x (D) x2 = -4y (E) 1y - 122 = 41x - 12 (F) 1x + 122 = 41y + 12 (G) 1y - 122 = -41x - 12 (H) 1x + 122 = -41y + 12

In Problems 1118, the graph of a parabola is given. Match each graph to its equation. (A) y2 = 4x (B) x2 = 4y (C) y2 = -4x (D) x2 = -4y (E) 1y - 122 = 41x - 12 (F) 1x + 122 = 41y + 12 (G) 1y - 122 = -41x - 12 (H) 1x + 122 = -41y + 13

In Problems 1118, the graph of a parabola is given. Match each graph to its equation. (A) y2 = 4x (B) x2 = 4y (C) y2 = -4x (D) x2 = -4y (E) 1y - 122 = 41x - 12 (F) 1x + 122 = 41y + 12 (G) 1y - 122 = -41x - 12 (H) 1x + 122 = -41y + 14

In Problems 1118, the graph of a parabola is given. Match each graph to its equation. (A) y2 = 4x (B) x2 = 4y (C) y2 = -4x (D) x2 = -4y (E) 1y - 122 = 41x - 12 (F) 1x + 122 = 41y + 12 (G) 1y - 122 = -41x - 12 (H) 1x + 122 = -41y + 15

In Problems 1118, the graph of a parabola is given. Match each graph to its equation. (A) y2 = 4x (B) x2 = 4y (C) y2 = -4x (D) x2 = -4y (E) 1y - 122 = 41x - 12 (F) 1x + 122 = 41y + 12 (G) 1y - 122 = -41x - 12 (H) 1x + 122 = -41y + 16

In Problems 1118, the graph of a parabola is given. Match each graph to its equation. (A) y2 = 4x (B) x2 = 4y (C) y2 = -4x (D) x2 = -4y (E) 1y - 122 = 41x - 12 (F) 1x + 122 = 41y + 12 (G) 1y - 122 = -41x - 12 (H) 1x + 122 = -41y + 17

In Problems 1118, the graph of a parabola is given. Match each graph to its equation. (A) y2 = 4x (B) x2 = 4y (C) y2 = -4x (D) x2 = -4y (E) 1y - 122 = 41x - 12 (F) 1x + 122 = 41y + 12 (G) 1y - 122 = -41x - 12 (H) 1x + 122 = -41y + 18

In Problems 1118, the graph of a parabola is given. Match each graph to its equation. (A) y2 = 4x (B) x2 = 4y (C) y2 = -4x (D) x2 = -4y (E) 1y - 122 = 41x - 12 (F) 1x + 122 = 41y + 12 (G) 1y - 122 = -41x - 12 (H) 1x + 122 = -41y + 19

Focus at 14, 02; vertex at 10, 02

Focus at 10, 22; vertex at 10, 02

Focus at 10, -32; vertex at 10, 02

Focus at 1 -4, 02; vertex at 10, 02

Directrix the line y = - 1 2 ; vertex at 10, 02

Focus at 10, -12; directrix the line y = 1

Directrix the line y = - 1 2 ; vertex at 10, 02

Directrix the line x = - 1 2 ; vertex at 10, 02

Vertex at 10, 02; axis of symmetry the y-axis; containing the point 12, 32

Vertex at 10, 02; axis of symmetry the x-axis; containing the point 12, 32

Vertex at 12, -32; focus at 12, -52

Vertex at 14, -22; focus at 16, -22

Vertex at 1 -1, -22; focus at 10, -22

Vertex at 1 -1, -22; focus at 10, -22

In Problems 1936, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.

Focus at 12, 42; directrix the line x = -4

Focus at 1 -3, -22; directrix the line x = 1

Focus at 1 -4, 42; directrix the line y = -2

In Problems 3754, find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility

In Problems 3754, find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility

In Problems 3754, find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility

In Problems 3754, find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility

In Problems 3754, find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility

In Problems 3754, find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility

In Problems 3754, find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility

In Problems 3754, find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility

In Problems 3754, find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility

In Problems 3754, find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility

In Problems 3754, find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility

In Problems 3754, find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility

In Problems 3754, find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility

In Problems 3754, find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility

In Problems 3754, find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility

In Problems 3754, find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility

In Problems 3754, find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility

In Problems 3754, find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility

In Problems 5562, write an equation for each parabola.

In Problems 5562, write an equation for each parabola.

In Problems 5562, write an equation for each parabola.

In Problems 5562, write an equation for each parabola.

In Problems 5562, write an equation for each parabola.

In Problems 5562, write an equation for each parabola.

In Problems 5562, write an equation for each parabola.

In Problems 5562, write an equation for each parabola.

A satellite dish is shaped like a paraboloid of revolution. The signals that emanate from a satellite strike the surface of the dish and are reflected to a single point, where the receiver is located. If the dish is 10 feet across at its opening and 4 feet deep at its center, at what position should the receiver be placed?

A cable TV receiving dish is in the shape of a paraboloid of revolution. Find the location of the receiver, which is placed at the focus, if the dish is 6 feet across at its opening and 2 feet deep.

The reflector of a flashlight is in the shape of a paraboloid of revolution. Its diameter is 4 inches and its depth is 1 inch. How far from the vertex should the light bulb be placed so that the rays will be reflected parallel to the axis?

A sealed-beam headlight is in the shape of a paraboloid of revolution. The bulb, which is placed at the focus, is 1 inch from the vertex. If the depth is to be 2 inches, what is the diameter of the headlight at its opening?

The cables of a suspension bridge are in the shape of a parabola, as shown in the figure. The towers supporting the cable are 600 feet apart and 80 feet high. If the cables touch the road surface midway between the towers, what is the height of the cable from the road at a point 150 feet from the center of the bridge?

The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cable are 400 feet apart and 100 feet high. If the cables are at a height of 10 feet midway between the towers, what is the height of the cable at a point 50 feet from the center of the bridge?

A searchlight is shaped like a paraboloid of revolution. If the light source is located 2 feet from the base along the axis of symmetry and the opening is 5 feet across, how deep should the searchlight be?

A searchlight is shaped like a paraboloid of revolution. If the light source is located 2 feet from the base along the axis of symmetry and the depth of the searchlight is 4 feet, what should the width of the opening be?

A searchlight is shaped like a paraboloid of revolution. If the light source is located 2 feet from the base along the axis of symmetry and the depth of the searchlight is 4 feet, what should the width of the opening be?

A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 4 inches across at its opening and is 3 inches deep, where will the collected light be concentrated?

A bridge is built in the shape of a parabolic arch. The bridge has a span of 120 feet and a maximum height of 25 feet. See the illustration. Choose a suitable rectangular coordinate system and find the height of the arch at distances of 10, 30, and 50 feet from the center.

A bridge is to be built in the shape of a parabolic arch and is to have a span of 100 feet. The height of the arch a distance of 40 feet from the center is to be 10 feet. Find the height of the arch at its center.

The Gateway Arch in St. Louis is often mistaken to be parabolic in shape. In fact, it is a catenary, which has a more complicated formula than a parabola. The Arch is 625 feet high and 598 feet wide at its base. (a) Find the equation of a parabola with the same dimensions. Let x equal the horizontal distance from the center of the arc. (b) The following table gives the height of the Arch at various widths; find the corresponding heights for the parabola found in (a).

Show that an equation of the form Ax2 + Ey = 0, A 0, E 0 is the equation of a parabola with vertex at 10, 02 and axis of symmetry the y-axis. Find its focus and directrix.

Show that an equation of the form Cy2 + Dx = 0, C 0, D 0 is the equation of a parabola with vertex at 10, 02 and axis of symmetry the x-axis. Find its focus and directrix.

Show that the graph of an equation of the form Ax2 + Dx + Ey + F = 0, A 0 (a) Is a parabola if E 0. (b) Is a vertical line if E = 0 and D2 - 4AF = 0. (c) Is two vertical lines if E = 0 and D2 - 4AF 7 0. (d) Contains no points if E = 0 and D2 - 4AF 6 0.

Show that the graph of an equation of the form Cy2 + Dx + Ey + F = 0, C 0 (a) Is a parabola if D 0. (b) Is a horizontal line if D = 0 and E2 - 4CF = 0. (c) Is two horizontal lines if D = 0 and E2 - 4CF 7 0. (d) Contains no points if D = 0 and E2 - 4CF 6 0. W