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Hint

1

Circle

(x-h)²+(y-k)²=r²

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2

Area of a Circle

*πr²*

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3

Degenerate Circle

(x-h)²+(y-k)²=0

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4

How can you tell if an equation is a circle without completing the square?

both variables are squared, somewhere in the equation

both x² and y² have exactly the same coefficient and the same sign

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5

Parabola (up/down)

y= a(x - h)² +k

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6

Parabola (left/right)

x= a(y - k)² +h

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7

Parabola (a)

a = 1/4c

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8

Parabola (c)

c = 1/4a

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9

Length of Latus Rectum (parabola)

I 1/a I = I 4c I

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10

C= dist. from . . .

**vertex** to **focus** or from **vertex** to **directrix**

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11

How can you tell if an equation is a parabola without completing the square?

only x or y is squared, but not both

if x is squared, then the graph goes up (a>0) or down (a<0)

if y is squared, then the graph goes right (a>0) or left (a<0)

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12

Ellipses formula (stretched horizontally)

__(x - h)²__ + __(y - k)²__ = 1

a² b²

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13

Ellipses formula (stretched vertically)

__(y - k)²__ + __(x - h)²__ = 1

a² b²

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14

Area of interior of ellipse

*πab*

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15

Sum of focal radii

2a

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16

length of major axis (ellipses)

2a

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17

length of minor axis

2b

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18

C= distance from . . .

**center** to each of the** foci**

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19

a²= (ellipses)

b² + c²

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20

How do you know if an equation is an ellipse without completing the square?

both of the variables are squared, somewhere in the equation

coefficients of x² and y² are different

signs of the coefficients of x² and y² are the same

the square root of the number under the “x” term will indicate the horizontal stretch

the square root of the number under the “y” term will indicate the vertical stretch

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21

Hyperbola formula (left/right)

[(x - h)²/ a²] - [(y - k)²/ b²] = 1

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22

hyperbola formula (up/down)

[(y - k)²/ a²] - [(x - h)²/ b²] = 1

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23

Difference of focal radii

2a

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24

c= distance from . . . . (hyperbola)

**center **to each **focus**

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25

c²=

a² + b²

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26

How do you know if an equation is a hyperbola without completing the square?

both variables are squared, somewhere in the equation

coefficients of x² and y² may be the same or may be different

signs of coefficients of x² and y² are different

if the

*x*term is positive/first, then the graph is “stretched” horizontally, if the*y*term is positive/first then the graph is “stretched” vertically

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27

Degenerate Hyperbola

[(x - h)²/ a²] - [(y - k)²/ b²] = 0

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28

Degenerate Ellipse

[(x - h)²/ a²] + [(y - k)²/ b²] = 0

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