Conic Sections Math Formulas Sheet
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1
2Math Formulas: Conic Sections
The Parabola Formulas
The standard formula of a parabola
2
1.
y
= 2 p x
Parametric equations of the parabola:
2
x = 2 p t
2.
y = 2 p t
2
Tangent line in a point D(x
, y
) of a parabola y
= 2px is :
0
0
3.
y
y = p (x + x
)
0
0
Tangent line with a given slope m:
p
4.
y = m x +
2m
Tangent lines from a given point
Take a fixed point P (x
, y
). The equations of the tangent lines are:
0
0
y
y
= m
(x
x
)
0
1
0
y
y
= m
(x
x
)
0
2
0
2
y
+
y
2px
0
0
5.
0
m
=
1
2x
0
2
y
y
2px
0
0
0
m
=
2
2x
0
The Ellipse Formulas
The set of all points in the plane, the sum of whose distances from two fixed points, called the foci, is a
constant.
The standard formula of a ellipse:
2
2
x
y
6.
+
= 1
2
2
a
b
Parametric equations of the ellipse:
x = a cos t
7.
y = b sin t
Tangent line in a point D(x
, y
) of a ellipse:
0
0
x
x
y
y
0
0
8.
+
= 1
2
2
a
b
Eccentricity of the ellipse:
2
2
a
b
9.
e =
a
Foci of the ellipse:
1
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