General equation of circle Note:
Parabolic standard equation
Basic formula of parabola: (a≠0),
Placed in a plane rectangular coordinate system
When a> is 0, the opening is upward.
When a< is 0, the opening is downward.
(a=0 is a linear function of one variable)
C>0, the function image intersects with the positive direction of Y axis.
C<0, the function image intersects with the negative direction of Y axis.
When c = 0, the parabola passes through the origin.
When b = 0, the axis of symmetry of parabola is the Y axis.
(Of course, this function is linear when a=0 and b≠0).
There are also vertex formulas y = a (x+h) * 2+k, (h, k) = (-b/(2a), (4ac-b 2)/(4a)).
That is, y equals a times the square of (x+h)+K.
-h is x of vertex coordinates.
K is y of vertex coordinates.
Generally used to find the maximum, minimum and symmetry axis.
Parabolic standard equation: y 2 = 2px (p > 0)
It means that the focus of parabola is on the positive semi-axis of X, the focal coordinate is (p/2,0), and the directrix equation is x=-p/2.
Since the focus of parabola can be on any semi-axis, there is a standard equation * * * Sphere volume = (4/3) π (r 3).
Area = π (r 2)
Perimeter =2πr =πd
Standard equation of a circle Note: (a, b) is the center coordinate.
General equation of circle Note: According to the standard elliptic equation, the major axis A and minor axis B are λ=(a-b)/(a+b).
Ellipse circumference l = π (a+b) (1+λ 2/4+λ 4/64+λ 6/256+25λ 8/16384+...).
Simplification: L≈π[ 1.5(a+b)- sqrt(ab)]
Or l ≈ π (a+b) (64-3λ 4)/(64-16λ 2) Ellipse area formula: S=πab.
Ellipse area theorem: the area of an ellipse is equal to π times the product of the major semi-axis length (a) and the minor semi-axis length (b) of an ellipse.
Although there is no ellipse πT in the above formula of ellipse circumference sum area, these two formulas are all derived from ellipse πT .. Constant is the body, so it can be used.
Volume calculation formula of ellipsoid long radius * short radius * ellipse π height