8.08, part 1

1. find the vertex, focus, directrix, and focal width of the parabola.
negative 1 divided by 16 times x squared = y

a) vertex: (0, 0); focus: (0, -4); directrix: y = 4; focal width: 16
b) vertex: (0, 0); focus: (-8, 0); directrix: x = 4; focal width: 64
c) vertex: (0, 0); focus: (0, 4); directrix: y = -4; focal width: 4
d) vertex: (0, 0); focus: (0, -4); directrix: y = 4; focal width: 64

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

a) y = negative 1 divided by 32 x2
b) y2 = -32x
c) y2 = -8x
d) y = negative 1 divided by 8 x2

3. find the standard form of the equation of the parabola with a focus at (5, 0) and a directrix at x = -5.

a) y = 1 divided by 20 x2
b) 20y = x2
c) x = 1 divided by 20 y2
d) y2 = 20x

4. a radio telescope has a parabolic surface, as shown below.
a parabola opening up with vertex at the origin is graphed on the coordinate plane. the height of the parabola from top to bottom is 1 meter and its width from left to right is 8 meters.

if the telescope is 1 m deep and 8 m wide, how far is the focus from the vertex?

a) 1 m
b) 2 m
c) 4 m
d) 16 m

5. find the center, vertices, and foci of the ellipse with equation x squared divided by 36 plus y squared divided by 100 = 1.

a) center: (0, 0); vertices: (0, -10), (0, 10); foci: (0, -8), (0, 8)
b) center: (0, 0); vertices: (-10, 0), (10, 0); foci: (0, -6), (0, 6)
c) center: (0, 0); vertices: (-10, 0), (10, 0); foci: (-8, 0), (8, 0)
d) center: (0, 0); vertices: (0, -10), (0, 10); foci: (-6, 0), (6, 0)

6. find the center, vertices, and foci of the ellipse with equation 3x2 + 7y2 = 21.

a) center: (0, 0); vertices: the point negative square root of seven comma zero and the point square root of seven comma zero ; foci: (-2, 0), (2, 0)
b) center: (0, 0); vertices: (-7, 0), (7, 0); foci: ordered pair negative 2 square root 10 comma 0 and ordered pair 2 square root 10 comma 0
c) center: (0, 0); vertices: the point zero comma negative square root of seven and the point zero comma square root of seven. ; foci: (0, -2), (0, 2)
d) center: (0, 0); vertices: (0, -7), (0, 7); foci: ordered pair 0 comma negative 2 square root 10 and ordered pair 0 comma 2 square root 10

7. graph the ellipse with equation
x squared divided by 4 plus y squared divided by 49 = 1.

a) a horizontal ellipse is shown on the coordinate plane centered at the origin with vertices at negative 7, 0 and 7, 0 and minor axis endpoints at 0, 2 and 0, negative 2.
b) a vertical ellipse is shown on the coordinate plane centered at the origin with vertices at 0, 7 and 0, negative 7 and minor axis endpoints at negative 2, 0 and 2, 0.
c) a horizontal ellipse is shown on the coordinate plane centered at (2, 7) with vertices at negative 5, 7 and 9, 7 and minor axis endpoints at 2, 9 and 2, 5.
d) a vertical ellipse is shown on the coordinate plane centered at 2, 7 with vertices at 2, 14 and 2, 0 and minor axis endpoints at 0, 7 and 4, 7.

8. find an equation in standard form for the ellipse with the vertical major axis of length 18 and minor axis of length 6.

a) x squared divided by 81 plus y squared divided by 9 = 1
b) x squared divided by 9 plus y squared divided by 3 = 1
c) x squared divided by 9 plus y squared divided by 81 = 1
d) x squared divided by 3 plus y squared divided by 9 = 1

9. find the vertices and foci of the hyperbola with equation quantity x plus 4 squared divided by 9 minus the quantity of y minus 5 squared divided by 16 = 1.

a) vertices: (5, 0), (5, -8); foci: (5, -8), (5, 0)
b vertices: (5, -1), (5, -7); foci: (5, -9), (5, 1)
c) vertices: (-1, 5), (-7, 5); foci: (-9, 5), (1, 5)
d) vertices: (0, 5), (-8, 5); foci: (-8, 5), (0, 5)

10. graph the hyperbola with equation quantity x plus 2 squared divided by 49 minus the quantity of y plus 3 squared divided by 4 = 1.

a) a vertical hyperbola is shown on the coordinate plane centered at 2, 3 with vertices at 2, 10 and 2, negative 4.
b) a horizontal hyperbola is shown on the coordinate plane centered at the origin with vertices at negative 7, 0 and 7, 0.
c) a horizontal hyperbola is shown on the coordinate plane centered at negative 2, negative 3 with vertices at negative 9, negative 3 and 5, negative 3.