# Conic Sections

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Horizontal Ellipse: vertices

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## Tags and Description

### 49 Terms

1

Horizontal Ellipse: vertices

(h ± a, k)

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2

Horizontal Ellipse: foci

(h ± c, k)

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3

Vertical Ellipse: vertices

(h, k ± a)

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4

Vertical Ellipse: foci

(h, k ± c)

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5

Horizontal Hyperbola: vertices

(h ± a, k)

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6

Horizontal Hyperbola: foci

(h ± c, k)

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7

Vertical Hyperbola: vertices

(h, k ± a)

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8

Vertical Hyperbola: foci

(h, k ± c)

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9

Horizontal Hyperbola: slope of asymptotes

±b/a + h

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10

Vertical Ellipse: slope of asymptotes

±a/b + k

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11

Ellipse: Find c

c² = a² - b²

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12

Hyperbola: Find c

c² = a² + b²

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13

standard vertical ellipse

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14

standard horizontal ellipse

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15

standard vertical hyperbola

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16

standard horizontal hyperbola

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17

standard circle

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18

standard vertical parabola

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19

standard horizontal parabola

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20

Parabola: End points of latus rectum

move parallel to directrix, 2p in either direction from the focus

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21

ID: 3x² + 9y² -6x + 18y = 0

ellipse

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22

ID: 3x² - 9y² -6x + 18y = 0

hyperbola

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23

ID: 3x² + 3y² -6x + 18y = 0

circle

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24

ID: 3x² -6x + 18y = 0

parabola

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25

The definition of a conic

Graphs that are created by slicing a cone

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26

The equation of a vertical parabola with vertex at (0,0)

x^2 = 4py

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27

The equation of a horizontal parabola with vertex at (0,0)

y^2 = 4px

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28

What "p" represents in a parabola

The distance from the vertex to the focus AND the distance from the vertex to the directrix

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29

The direction this parabola opens: x^2 = -8y

Down

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30

The direction this parabola opens: y^2 = 12x

Right

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31

The focus in this parabola: x^2 = 16y

(0, 4)

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32

The directrix in this parabola: y^2 = -4x

x = 1

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33

The value of "p" in this parabola: x^2 = -6x

p = 3/2

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34

The meaning of "a" in an ellipse

The distance from center to vertex

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35

The meaning of "c" in an ellipse

The distance from center to focus

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36

The formula relating a, b, and c in an ellipse

a^2 - b^2 = c^2

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37

How you decide whether an ellipse is vertical or horizontal looking at its equation

Find the largest denominator (which is a^2). If it is under the x, it's horizontal. If it's under the y, it's vertical.

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38

The vertices of x^2/9 + y^2/36 = 1

Vertices are (0, 6) and (0, -6)

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39

The c value for x^2/16 + y^2/49 = 1

c = square root of 33

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40

The equation of a vertical hyperbola centered at (0, 0)

y^2/a^2 - x^2/b^2 = 1

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41

The equation of a horizontal hyperbola centered at (0, 0)

x^2/a^2 - y^2/b^2 = 1

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42

The way to determine whether a hyperbola is vertical or horizontal by looking at its equation

Look at what variable is first (positive). If x is first, it's horizontal. If y is first, it's vertical.

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43

The meaning of "a" in a hyperbola

The distance from center to vertex

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44

The meaning of "c" in a hyperbola

The distance from center to focus

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45

The equation relating a, b, and c in a hyperbola

a^2 + b^2 = c^2

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46

Is this hyperbola vertical or horizontal? y^2/4 - x^2/16 = 1

Vertical (y is first)

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47

What are the vertices in this hyperbola? x^2/25 - y^2/9 = 1

Vertices are (5, 0) and (-5, 0)

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48

What are the slopes of the asymptotes? x^2/36 - y^2/100 = 1

This is a horizontal hyperbola so we use b/a which is 10/6 or 5/3 (+ and -)

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49

Where are the foci in this hyperbola? y^2/36 - x^2/64 = 1

First, a^2 + b^2 = 100, so c = 10. Since this is a vertical hyperbola (y is first), the foci are (0, 10) and (0, -10)

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