8.07a, part 1

1. find the vertex, focus, directrix, and focal width of the parabola. (1 point)
negative 1 divided by 40 x squared equals y

a) vertex: (0, 0); focus: (0, -10); directrix: y = 10; focal width: 160
b) vertex: (0, 0); focus: (-20, 0); directrix: x = 10; focal width: 160
c) vertex: (0, 0); focus: (0, -10); directrix: y = 10; focal width: 40
d) vertex: (0, 0); focus: (0, 10); directrix: y = -10; focal width: 10

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

a)y2 = -2x
b) y2 = -8x
c) y equals negative 1 divided by 8 x squared
d) y equals negative 1 divided by 2 x squared

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

a) y equals negative 1 divided by 32 x squared
b) y2 = 16x
c) 16y = x2
d) x equals negative 1 divided by 32 y squared

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.
a parabola opening down with vertex at the origin is graphed on the coordinate plane. the height of the parabola from top to bottom is 84 feet and its width from left to right is 42 feet.

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

a) y2 = -21x
b) x2 = -21y
c) x2 = -5.3y
d) y2 = -5.3x

5. find the center, vertices, and foci of the ellipse with equation x squared divided by 81 plus y squared divided by 225 equals 1 .

a) center: (0, 0); vertices: (-15, 0), (15, 0); foci: (0, -9), (0, 9)
b) center: (0, 0); vertices: (0, -15), (0, 15); foci: (-9, 0), (9, 0)
c) center: (0, 0); vertices: (0, -15), (0, 15); foci: (0, -12), (0, 12)
d) center: (0, 0); vertices: (-15, 0), (15, 0); foci: (-12, 0), (12, 0)

6. find the center, vertices, and foci of the ellipse with equation 2x2 + 8y2 = 16.

a) center: (0, 0); vertices: the point zero comma negative two square root two and the point zero comma 2 square root two ; foci: ordered pair 0 comma negative square root 6 and ordered pair 0 comma square root 6
b) center: (0, 0); vertices: (-8, 0), (8, 0); foci: ordered pair negative 2 square root 15 comma 0 and ordered pair 2 square root 15 comma 0
c) center: (0, 0); vertices: (0, -8), (0, 8); foci: ordered pair 0 comma negative 2 square root 15 and ordered pair 0 comma 2 square root 15
d) center: (0, 0); vertices: the point negative square root six comma zero and the point square root six comma zero ; foci: ordered pair negative square root 6 comma 0 and ordered pair square root 6 comma 0

7. graph the ellipse with equation x squared divided by 36 plus y squared divided by 49 equals 1 .

a) a horizontal ellipse is shown on the coordinate plane centered at the origin with vertices at the point negative seven comma zero and the point seven comma zero. the minor axis has endpoints at zero comma six and zero comma negative six.
b) a vertical ellipse is shown on the coordinate plane centered at the origin with vertices at the point zero comma seven and zero comma negative seven. the minor axis has endpoints at negative six comma zero and six comma zero.
c) a horizontal ellipse is shown on the coordinate plane centered at (6, 7) with vertices at (–1, 7) and (13, 7) and minor axis endpoints at (6, 13) and (6, 1).
d) a horizontal ellipse is shown on the coordinate plane centered at the point six comma seven with vertices at the point negative one comma seven and thirteen comma seven. the minor axis has endpoints at six comma thirteen and six comma one.

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

a) x squared divided by 25 plus y squared divided by 16 equals 1
b) x squared divided by 5 plus y squared divided by 4 equals 1
c) x squared divided by 4 plus y squared divided by 5 equals 1
d) x squared divided by 16 plus y squared divided by 25 equals 1

9. find the vertices and foci of the hyperbola with equation quantity x plus 5 squared divided by 36 minus the quantity of y plus 1 squared divided by 64 equals 1 .

a) vertices: (-1, 3), (-1, -13); foci: (-1, -13), (-1, 3)
b) vertices: (3, -1), (-13, -1); foci: (-13, -1), (3, -1)
c) vertices: (-1, 1), (-1, -11); foci: (-1, -15), (-1, 5)
d) vertices: (1, -1), (-11, -1); foci: (-15, -1), (5, -1)