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Equation adds x²/a² and y²/b²=1
A fixed points
Vertices of an Ellipse
The endpoints on the major axis of an ellipse.
Co-vertices of an Ellipse
The endpoints of the minor axis of an ellipse.
Foci of Ellipse
c^2 = a^2 - b^2
Standard Form Equation of an Ellipse
(x-h)^2/a^2 + (y-k)^2/b^2 = 1; horizontal; a>b>o.
Equation subtracts x²/a and y²/b=1; x and y coefficients have different signs.
The axis that goes through the vertices of a hyperbola.
Standard Form Equation of an Hyperbola
(x-h)^2/a^2 - (y-h)^2/b^2 = 1; horizontal; Asymptote: y=+/-bx/a
Foci of Hyperbola
c^2 = a^2 + b^2
the graph of a quadratic function
|a| = 1/4c
Focus/Directrix of a Parabola
Standard Form Equation of a Parabola
y = a(x-h)^2 + k; Vertical; vertex (h,k)
Standard form (Circle)
(x-h)^2 + (y-k)^2 = r^2
Center of a circle
Standard form (Parabola)
y = (1/4c)(x-h)^2+k
Vertex of a parabola
Axis Of symmetry
Focus of a Parabola
Ab. Value 4C
Standard form (Ellipse)
((x - h)^2 / a^2) + ((y - k)^2 / b^2) = 1
Center of a ellipse
Major Axis (Ellipse)
Endpoints of the major axis
Endpoints of the minor axis
Foci are on the major axis 'c' units from the center
Width of ellipse at foci
Transversal axis (hyperbola)
Conjugate axis (hyperbola)
Vertices (hyperbola )
endpoints of the transversal axis
c^2 = A^2 + b^2
The squared terms have equal coefficients
Defining an equation to produce a circle
The standard form for a circle
Each regular polygon has a center because it can be inscribed in a circle.
From center to a point on the circle.
Defining an equation to produce an ellipse
The squared terms have different coefficients with the same sign
Standard equation of ellipse
Equation for finding the foci of an ellipse
Defining an equation to produce a hyperbola
The squared terms have coefficients with different signs
standard equation of a hyperbola
Standard form form a hyperbola when the x-term is negative
(h,k) in the standard forms for a hyperbola represents...
The equation for finding the foci of a hyperbola
The equation for finding the asymptotes of a hyperbola
The asymptote of a hyperbola represents
lines that restrict the width of a given hyperbolic equation
The transverse axis of a parabola
The sum of the distances from the focus to points on the parabola perpendicular to the axis of symmetry from the focus. It always equals 4p
Defining an equation to produce a parabola
One term is squared and the other is not
The standard form for a parabola when the x-term is squared
The standard form for a parabola when the y-term is squared
(h,k) in the standard forms for a parabola represents...
The distance from the vertex from the focus and the directrix
The directrix of a parabola
A line perpendicular to the axis of symmetry and a distance of |p| away from the vertex
the parabola faces upwards
Under the conditions p+ and x²
the parabola faces downwards
Under the conditions p- and x²
Under the conditions p+ and y²
the parabola faces to the right
Under the conditions p- and y²
The parabola faces to the left
As p gets smaller...
the parabola will tighten