Studied by 0 peopleConic section
A curve generated by intersecting a right circular cone with a plane.
Circle
A simple closed curve, with a set of all points at a constant distance from a fixed center pointer, in the same plane.
Parabola
A curve formed by the intersection of a cone with a plane parallel to a straight line in its surface.
Ellipse
A regular oval shape.
Hyperbola
Two-branched open curve, a conic section, produced by the intersection of a circular cone and a plane that cuts both nappes (see cone) of the cone.
( x - h )^2 + ( y - k )^2 = r^2
Equation of circle.
( x - h )^2 = 4p( y - k ) or ( y - k )^2 = 4p( x - h )
Equation of parabolas.
( x - h )^2 / a^2 - ( y - k )^2 / b^2 = 1
Equation of hyperbolas.
( x - h )^2 / a^2 + ( y - k )^2 / b^2 = 1
Equation of ellipses.
y = mx + b
Equation of a line.
m1 = m2
The slope of parallel lines.
m2 = -1 / m1
The slope of perpendicular lines.
square root ( x2 - x1 )^2 + ( y2 - y1 )^2
The distance formula
x = ( mx2 + nx1 ) / m + n ; y = ( my2 + ny1 ) / m + n
The general formula for points that partition line segments.
x = ( x1 + x2 ) / 2 ; y = ( y1 + y2 ) / 2
The midpoint formula.
x^2 = 4py
The general formula of the parabola with horizontal directrix.
y^2 = 4px
The general formula of the parabola with vertical directrix.
y = k - p
The directrix of the parabola with horizontal directrix.
x = h - p
The directrix of the parabola with vertical directrix.
F ( h ; k + p )
The focus of the parabola with horizontal directrix.
F ( h + p ; k )
The focus of the parabola with vertical directrix.
( y2 - y1 ) / ( x2 - x1 )
The formula of a slope of a line.
Note
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