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Level 499

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Ellipse

Equation adds x²/a² and y²/b²=1

Focus

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.

Hyperbola

Equation subtracts x²/a and y²/b=1; x and y coefficients have different signs.

Transverse Axis

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

Parabola

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

(h, k)

Center of a circle

Distance Formula

(Square root)(x2-x1)^2+(y2-y1)^2

Standard form (Parabola)

y = (1/4c)(x-h)^2+k

(Y): (h,k)

Vertex of a parabola

x=h

Axis Of symmetry

Y: (h,k+c)

Focus of a Parabola

Directrix

y=k-c

Laterus Rectum

Ab. Value 4C

Standard form (Ellipse)

((x - h)^2 / a^2) + ((y - k)^2 / b^2) = 1

(h,k)

Center of a ellipse

2a

Major Axis (Ellipse)

2b

Minor Axis(ellipse)

vertices (ellipse)

Endpoints of the major axis

Co-Verticies (ellipse)

Endpoints of the minor axis

Foci (Ellipse)

Foci are on the major axis 'c' units from the center

LR (ellipse)

Width of ellipse at foci

2b^2/a

LR (Hyperbola)

2a

Transversal axis (hyperbola)

2b

Conjugate axis (hyperbola)

Vertices (hyperbola )

endpoints of the transversal axis

Foci (hyperbola)

c^2 = A^2 + b^2

Circle

r= asin(theta)

The squared terms have equal coefficients

Defining an equation to produce a circle

(x-h)²+(y-k)²=r²

The standard form for a circle

Center

Each regular polygon has a center because it can be inscribed in a circle.

radius

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

(x-h)²/a²+(y-k)²/b²=1

Standard equation of ellipse

c²=|a²-b²|

Equation for finding the foci of an ellipse

Defining an equation to produce a hyperbola

The squared terms have coefficients with different signs

(x-h)²/a²-(y-k)²/b²=1

standard equation of a hyperbola

-(x-h)²/a²+(y-k)²/b²=1

Standard form form a hyperbola when the x-term is negative

The center

(h,k) in the standard forms for a hyperbola represents...

c²=a²+b²

The equation for finding the foci of a hyperbola

(y-k)=±(b/a)(x-h)

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

4p(y-k)=(x-h)²

The standard form for a parabola when the x-term is squared

4p(x-h)=(y-k)²

The standard form for a parabola when the y-term is squared

the vertex

(h,k) in the standard forms for a parabola represents...

|p|

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