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a circle

If A and B are equal it's...

equal

having the same value

an ellipse

If A and B are both positive and different values it's...

both positive and different values

Conditions of A/B for an ellipse

a hyperbola

If A or B is negative it's...

one is negative

Conditions of A/B for a hyperbola

a parabola

If A or B is zero, it's...

one is zero

Conditions of A/B for a parabola

(x-h)²+(y-k)²=r²

equation of a circle (in standard form)

x²+y²=r²

What is the equation of a circle if the center is (0,0)

Ellipse

the set of all points such that the sum of the distances from the foci is constant

(x-h)²+(y-k)²=1

standard form (of an ellipse) with (x) having the bigger value for (a)

2a

Major (longer) axis on an ellipse is...

Foci points on an ellipse

±c from center (on major axis)

bigger

ellipse a2 always...

2b

Minor (shorter) axis on an ellipse is...

c²=a²-b²

How do you find (c) on an ellipse?

(x-h)²-(y-k)²=1

Standard form (of a hyperbola) with (x) first

(y-k)²-(x-h)²=1

Standard form (of a hyperbola) with (y) first

±y/x

How do you find the slope for a hyperbola?

±a from the center (on major axis)

How do you find the vertices of a hyperbola?

±c from center (on major axis)

How do you find the foci points of a hyperbola?

none

amplitude of y=a tan bx

opposite of what is in the parentheses

How do you find the center for a parabola?

y=a(x-h)²+k

standard form (of a parabola) that goes up or down

x=a(y-k)²+h

Standard Equation of a Parabola

starts with y

What makes a parabola graph go up or down?

starts with x

What makes a parabola graph go right or left?

a is positive

What makes a parabola open up or right?

a is negative

horizontal flip on x-axis

axis of symmetry for a parabola

equation of the line that cuts the parabola in half

What is (p) in a parabola?

distance from the vertex to the focus

a= 1/4p

Formula for finding (p) in a parabola?

±p to the vertex

How do you find the focus point in a parabola?

narrower

The closer the focus and vertex are, the ______________________ the parabola.

wider

The farther the focus and vertex are, the ____________________________ the parabola.

(x-h)²+(y-k)²=r²

The standard form for a circle

(x-h)²=4p(y-k)

parabolic equation

elliptical equation

(x-h)²/a² + (y-k)²/b² =1

hyperbolic equation

(x-h)²/a² - (y-k)²/b² =1

(h,k)

parabolic vertex

(h,k+p)

parabolic focus

Directrix

y=k-c

x=h

Axis Of symmetry

p

focal length

|4p|

focal width

(h,k)

elliptical center

y=k

major axis

2a

major axis length

2b

minor axis length

(h±a,k)

elliptical vertex

(h±c,k)

elliptical foci

(h,k)

hyperbolic center

2a

transverse axis

2b

conjugate axis

Asymptotes

y=±b/a(x-h)+k

(h ,k+p)

(x-h)²=4p(y-k); Focus?

y=k-p

(x-h)²=4p(y-k); Directrix?

(y-k)²=4p(x-h); Focus?

(h+p, k)

x=h-p

(y-k)²=4p(x-h); Directrix?

(±a, 0)

(x²)/(a²) + (y²)/(b²) = 1; Vertices?

(0,±b)

(x²)/(a²) + (y²)/(b²) = 1; Y-ints?

(±c, 0)

(x²)/(a²) + (y²)/(b²) = 1; Foci?

(0,±a)

(x²)/(b²) + (y²)/(a²) = 1; V

(±b,0)

(x²)/(b²) + (y²)/(a²) = 1; x-int?

(0,±c)

(x²)/(b²) + (y²)/(a²) = 1; Foci?

2b

(x-h)²/a² + (y-k)²/b² = 1; Minor axis?

(h,k±a)

(x-h)²/b² + (y-k)²/a² = 1; Vertices?

2b

(x-h)²/b² + (y-k)²/a² = 1; Minor Axis?

(h,k±c)

(x-h)²/b² + (y-k)²/a² = 1;Foci

y= ±(b/a)x

(x²)/(a²) - (y²)/(b²) = 1 Asym

y = ±(a/b)x

(y²)/(a²) - (a²)/(b²) = 1 Asymq

y-k = ±(b/a)(x-h)

(x-h)²/a² - (y-k)²/b² = 1 Asym

(h, k±a)

(y-k)²/a² - (x-h)²/b² = 1 Vertices

y-k = ±(a/b)(x-h)

(y-k)²/a² - (x-h)²/b² = 1 Asym