Conics Test Flashcards

1
Q

How to tell if it is a circle

A

Both are squared and it equals a perfect square

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2
Q

How to graph a circle with the center at (0,0)

A

Identify the center
Identify the radius (r) by taking the square root of the thing the equation equals
Plot points based on the radius
(x,y) (-x,y) (y,x) (-y,x)

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3
Q

How to graph a circle with the center not at (0,0)

A

Identify the center
Identify the radius
Create two points with x as the same as the center and add and subtract the radius to y
Create two other points with y the same and add and subtract the radius to x

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4
Q

How to write the equation of a circle

A

Center: (h,k)
Point: (x,y)
Find the radius with the equation
r= √(x-h)²+ (y-k)²
r²= that without the square root
Write the whole equation (x-h)² + (y-k)² =r²

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5
Q

Horizontal Major Axis Ellipse Equation

A

(x-h)² / a² + (y-k)² / b² = 1

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6
Q

Vertical Major Axis Ellipse Equation

A

(x-h)² / b² + (y-k)² / a² = 1

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7
Q

Major Axis Ellipse

A

Both: 2a

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8
Q

Minor Axis Ellipse

A

Both: 2b

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9
Q

Horizontal Vertices Ellipse

A

(h +/- a, k)

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10
Q

Vertical Vertices Ellipse

A

(h, k +/- a)

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11
Q

Horizontal Co-vertices Ellipse

A

(h, k+/- b)

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12
Q

Vertical Co-vertices Ellipse

A

(h +/- b, k)

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13
Q

Horizontal Foci Ellipse

A

(h +/- c, k)

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14
Q

Vertical Foci Ellipse

A

(h, k +/- c)

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15
Q

Pythag. Relation Ellipse

A

c² = a² - b²

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16
Q

Horizontal Hyperbola Transverse Axis Equation

A

(x-h)² / a² - (y-k)² / b² =1

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17
Q

Vertical Hyperbola Transverse Axis Equation

A

(y-k)² / a² - (x-h)² / b² =1

18
Q

Focal Axis (Line through the Foci)

19
Q

Hyperbola Line connecting vertices (transverse axis)

20
Q

Line connecting co-vertices (conjugate axis)

21
Q

Horizontal vertices hyperbola

A

(h +/- a, k)

22
Q

Vertical Vertices Hyperbola

A

(h, k+/- a)

23
Q

Horizontal Co-vertices Hyperbola

A

(h, k+/- b)

24
Q

Vertical Co-vertices Hyperbola

A

(h +/- b, k)

25
Horizontal Foci Hyperbola
(h +/- c, k)
26
Vertical Foci Hyperbola
(h, k +/- c)
27
Hyperbola Asymptote Equation
Both: y-k = +/- b/a(x-h)
28
Hyperbola Pythag. Relation
c²= a²+b²
29
Vertical Equation of a Parabola
(x-h)² = 4p(y-k)
30
Horizontal Equation of a Parabola
(y-k)² = 4p(x-h)
31
Parabola Vertical Focus
(h, k+p)
32
Parabola Horizontal Focus
(h+p, k)
33
Parabola Vertical Directrix
y= k-p
34
Parabola Horizontal Directrix
x= h-p
35
p=
1/4a
36
a=
1/4p
37
Parabola Focal Length
Both: p
38
How to write the equation of a parabola
Determine whether the equation is horizontal or vertical Plug vertex (h,k) into the correct equation
39
40
Note: Make sure to find the center
Find the center by finding the letters and see what you can add and subtract to get the numbers in the ordered pairs