# Find The Vertex Focus Directrix And Focal Width Of The Parabola Vertex 0 0 Focus

Find the vertex, focus, directrix, and focal width of the parabola.

Vertex: (0, 0); Focus: (0, -10); Directrix: y = 10; Focal width: 160

Vertex: (0, 0); Focus: (-20, 0); Directrix: x = 10; Focal width: 160

Vertex: (0, 0); Focus: (0, -10); Directrix: y = 10; Focal width: 40

Vertex: (0, 0); Focus: (0, 10); Directrix: y = -10; Focal width: 10

Question 2

Find the standard form of the equation of the parabola with a focus at (0, -2) and a directrix at y = 2.

y2 = -2x

y2 = -8x

Question 3

Find the standard form of the equation of the parabola with a focus at (-8, 0) and a directrix at x = 8.

y2 = 16x

16y = x2

Question 4

A building has an entry the shape of a parabolic arch 84 ft high and 42 ft wide at the base, as shown below.

Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

y2 = -21x

x2 = -21y

x2 = -5.3y

y2 = -5.3x

Question 5

Find the center, vertices, and foci of the ellipse with equation .

Center: (0, 0); Vertices: (-15, 0), (15, 0); Foci: (0, -9), (0, 9)

Center: (0, 0); Vertices: (0, -15), (0, 15); Foci: (-9, 0), (9, 0)

Center: (0, 0); Vertices: (0, -15), (0, 15); Foci: (0, -12), (0, 12)

Center: (0, 0); Vertices: (-15, 0), (15, 0); Foci: (-12, 0), (12, 0)

Question 6

Find the center, vertices, and foci of the ellipse with equation 2×2 + 8y2 = 16.

Center: (0, 0); Vertices: ; Foci:

Center: (0, 0); Vertices: (-8, 0), (8, 0); Foci:

Center: (0, 0); Vertices: (0, -8), (0, 8); Foci:

Center: (0, 0); Vertices: ; Foci:

Question 7

Graph the ellipse with equation .

Question 8

Find an equation in standard form for the ellipse with the vertical major axis of length 10 and minor axis of length 8.

Question 9

Find the vertices and foci of the hyperbola with equation .

Vertices: (-1, 3), (-1, -13); Foci: (-1, -13), (-1, 3)

Vertices: (3, -1), (-13, -1); Foci: (-13, -1), (3, -1)

Vertices: (-1, 1), (-1, -11); Foci: (-1, -15), (-1, 5)

Vertices: (1, -1), (-11, -1); Foci: (-15, -1), (5, -1)

Question 10

Graph the hyperbola with equation .

Question 11

Find an equation in standard form for the hyperbola with vertices at (0, ±2) and foci at (0, ±11).

Question 12

Find an equation in standard form for the hyperbola with vertices at (0, ±8) and asymptotes at .

Question 13

Eliminate the parameter.

x = t – 3,

Question 14

Find the rectangular coordinates of the point with the polar coordinates .

Question 15

Find all polar coordinates of point P where P =  .

(1,  + 2nπ) or (-1,  + (2n + 1)π)

(1,  + (2n + 1)π) or (-1,  + 2nπ)

(1,  + nπ) or (-1, + nπ)

(1,  + 2nπ) or (-1,  + 2nπ)

Question 16

Determine two pairs of polar coordinates for the point (3, -3) with 0° ≤ θ < 360°.

(3 , 315°), (-3 , 135°)

(3 , 225°), (-3 , 45°)

(3 , 45°), (-3 , 225°)

(3 , 135°), (-3 , 315°)

Question 17

The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph.

[-5, 5] by [-5, 5]

r = 2 + 3 cos θ

r = 3 + 2 cos θ

r = 2 + 2 cos θ

r = 4 + cos θ

Question 18

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

r = 4 – 4 cos θ

No symmetry

x-axis only

y-axis only

Origin only

Question 19

A railroad tunnel is shaped like a semiellipse, as shown below.

The height of the tunnel at the center is 58 ft, and the vertical clearance must be 29 ft at a point 21 ft from the center. Find an equation for the ellipse.

Question 20

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

r = 4 cos 5θ