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Level 500

Conics II


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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