Conic Section Formulas Flashcards

0
Q

Distance formula

A

Sq. root of (x2 - x1)^2 + (y2 - y1)^2

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1
Q

Midpoint formula

A

(X1 + X2/2, y1 + y2/2)

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2
Q

Up and down parabola equation

A

Y= a(x - h)^2 + k

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3
Q

Left and right parabola equation

A

X= a(y - k)^2 + h

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4
Q

Vertex of parabolas

A

(h, k)

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5
Q

Axis of symmetry of up and down parabola

A

X = h

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6
Q

Focus of up and down parabola

A

(h, k + 1/4a)

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7
Q

Directrix of up and down parabola

A

y = k - 1/4a

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8
Q

Axis of symmetry of right and left parabola

A

Y = k

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9
Q

Focus of left and right parabola

A

(h + 1/4a, k)

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10
Q

Directrix of left and right parabola

A

X = h - 1/4a

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11
Q

If a<0 in a parabola

A

The parabola is either left or down

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12
Q

If a>0 in a parabola

A

The parabola is either up or right

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13
Q

Standard circle formula

A

(x - h)^2 + (y - k)^2 = r^2

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14
Q

Center of a circle

A

(h, k)

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15
Q

Radius of a circle

A

r

16
Q

Standard eq. Horizontal ellipse

A

(x - h)^2/ a^2 + (y - k)^2/b^2 = 1

17
Q

Foci of horizontal ellipse

A

(h +/- c, k)

18
Q

Length of major axis of ellipse

A

2a

19
Q

Length of minor axis of ellipse

A

2b

20
Q

Relationship of a/b/c of ellipse

A

A^2 - b^2 = c

21
Q

Standard eq. Of vertical ellipse

A

(x - h)^2/b^2 + (y - k)^2/ a^2 = 1

22
Q

Foci of vertical ellipse

A

(h, k+/- c)

23
Q

Standard eq. Of horizontal hyperbolas

A

(x - h)^2/a^2 - (y - k)^2/ b^2 = 1

24
Q

Vertices of horizontal hyperbola

A

(h +/- a, k)

25
Q

Foci of horizontal hyperbolas

A

(h +/-, k)

26
Q

Co- vertices of hyperbola

A

Same as vertices only a is b

27
Q

Length of transverse axis of hyperbola

A

2a

28
Q

Length of conjugate axis of hyperbola

A

2b

29
Q

Relationship between a b and c of hyperbola

A

a^2 + b^2 = c^2

30
Q

Standard equation of vertical hyperbola

A

(y - k)^2/ a^2 - (x - h)^2/ b^2 = 1

31
Q

Vertices of vertical hyperbola

A

(h, k +- a)

32
Q

Foci of vertical hyperbolas

A

(h, k+- c)

33
Q

Slope of horizontal asymptotes

A

+- b/a

34
Q

Slope of vertical asymptotes

A

+- a/b