Conic Section Formulas
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1Conic Section Formulas
PARABOLA______________________________________________________________________________
Vertical Axis
Horizontal Axis
2
2
(x-h)
= 4p(y-k)
(y-k)
= 4p(x-h)
Equation:
x = h
y = k
Axis of Symmetry:
(h, k)
(h, k)
Vertex:
(h, k+p)
(h+p, k)
Focus:
y = k-p
x = h-p
Directrix:
p>0 up, p<0 down
p>0 right, p<0 left
Direction of Opening:
ELLIPSE_________________________________________________________________________________
Major Axis Vertical
Major Axis Horizontal
2
2
2
2
(
)
(
)
(
)
(
)
x
h
y
k
x
h
y
k
1
1
Equation:
2
2
2
2
b
a
a
b
(h, k)
(h, k)
Center:
(h, k+a)
(h+a, k)
Vertices:
(h, k+c)
(h+c, k)
Foci:
2a = Length of Major Axis
Major Axis:
2b = Length of Minor Axis
Minor Axis:
2
2
2
where a > b > 0
Equation that Relates a,b,c:
a
b
c
e = c/a
Eccentricity:
HYPERBOLA_____________________________________________________________________________
Transverse Axis Vertical
Transverse Axis Horizontal
2
2
2
2
(
)
(
)
(
)
(
)
y
k
x
h
x
h
y
k
1
1
Equation:
2
2
2
2
a
b
a
b
(h, k)
(h, k)
Center:
(h, k+a)
(h+a, k)
Vertices:
(h, k+c)
(h+c, k)
Foci:
a
b
(
)
(
)
Asymptotes:
y
k
x
h
y
k
x
h
b
a
2
2
2
Equation that Relates a,b,c:
c
a
b
CIRCLE__________________________________________________________________________________
2
2
2
(x – h)
+ (y – k)
= r
Equation:
(h, k)
Center:
r
Radius:
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