Conic Sections
Consists of four geometric shapes (parabolas, circles, ellipses, and hyperbolas) that are actually the cross-sections of a right circular cone sliced by a plane
If A equals B
It's a circle
If A doesn't equal B (same signs)
It's an ellipse
If A doesn't equal B (different signs)
It's a hyperbola
General Form
A x2 + B y2 + C x+ D y + E = 0
Parabola
Is the set of points on the coordinate plane that are equidistant from a fixed point (focus) and fixed line (directrix)
Parabola's Standard Form (x2)
y = a ( x - h) 2 + k
Parabola's Standard Form (x2): vertex
( h , k )
Parabola's Standard Form (x2): focus
( h , k + c )
Parabola's Standard Form (x2): axis of symmetry
( x = h )
Parabola's Standard Form (x2): directrix
( y = k - c )
Axis of Symmetry
A line that cuts through the middle of the parabola, intersecting at the vertex
Vertex
Parabola's lowest point if graphs points up, highest point if graph points down
The Value C
The distance from the vertex to both the focus and directrix (measured along axis of symmetry); will always be POSITIVE
The Value A in the Standard Form
+/- (1/(4c))
Parabola's Standard Form (y2)
x = a ( y - k ) 2 + h
Parabola's Standard Form (y2) : Directrix
x = h - c
Parabola's Standard Form (y2): Focus
( h + c, k )
Parabola's Standard Form (y2): Axis of Symmetry
y = k
Circle
Is a set of points in the coordinate plane that are all the same distance (called the radius) from a fixed point (called the center)
Circle's Standard Form
( x - h ) 2 + (y - k ) 2 = r 2