Level 498
Level 500

#### 70 words 0 ignored

Ready to learn
Ready to review

## Ignore words

Check the boxes below to ignore/unignore words, then click save at the bottom. Ignored words will never appear in any learning session.

**Ignore?**

The definition of a conic

Graphs that are created by slicing a cone

4

The number of conics

Ancient Greeks

Who invented the conics

Parabola, circle, ellipse, hyperbola

The names of the conics

x^2 = 4py

The equation of a vertical parabola with vertex at (0,0)

y^2 = 4px

The equation of a horizontal parabola with vertex at (0,0)

What "p" represents in a parabola

The distance from the vertex to the focus AND the distance from the vertex to the directrix

The definition of a parabola

The set of points equidistant from a fixed point (the focus) and a fixed line (the directrix)

down

If a < 0, the parabola opens

Right

a positive exponent means the original decimal needs to move to the _______________________

(0, 4)

The focus in this parabola: x^2 = 16y

x = 1

The directrix in this parabola: y^2 = -4x

p = 3/2

The value of "p" in this parabola: x^2 = -6x

The definition of a circle

The set of points equidistant from a fixed point

x^2 + y^2 = r^2

The equation of a circle centered at (0,0)

radius = 9

The radius of this circle: x^2 + y^2 = 81

A fact we know about tangent lines and radii

A tangent line is always perpendicular to the radius at the point of tangency

slope of radius = 5/4

The slope of the tangent line to x^2 + y^2 = 25 at (4, 5)

The definition of an ellipse

The set of points such that the sum of the focal radii is a constant.

x^2/b^2 + y^2/a^2 = 1

The equation for a vertical ellipse centered at (0,0)

x^2/a^2 + y^2/b^2 = 1

The equation for a horizontal ellipse centered at (0,0)

The distance from center to vertex

The meaning of "a" in an ellipse

The meaning of "b" in an ellipse

The distance from center to endpoint (covertices)

The distance from center to focus

The meaning of "c" in an ellipse

a^2 - b^2 = c^2

The formula relating a, b, and c in an ellipse

How you decide whether an ellipse is vertical or horizontal looking at its equation

Find the largest denominator (which is a^2). If it is under the x, it's horizontal. If it's under the y, it's vertical.

Vertices are (0, 6) and (0, -6)

The vertices of x^2/9 + y^2/36 = 1

Endpoints are (0, 2) and (0, -2)

Endpoints (covertices) of x^2/25 + y^2/4 = 1

c = square root of 33

The c value for x^2/16 + y^2/49 = 1

The definition of a hyperbola

The set of points such that the absolute value of the difference of the focal radii is a constant.

y^2/a^2 - x^2/b^2 = 1

The equation of a vertical hyperbola centered at (0, 0)

x^2/a^2 - y^2/b^2 = 1

The equation of a horizontal hyperbola centered at (0, 0)

The way to determine whether a hyperbola is vertical or horizontal by looking at its equation

Look at what variable is first (positive). If x is first, it's horizontal. If y is first, it's vertical.

The distance from center to vertex

The meaning of "a" in a hyperbola

The distance from center to endpoints

The meaning of "b" in a hyperbola

The distance from center to focus

The meaning of "c" in a hyperbola

a^2 + b^2 = c^2

The equation relating a, b, and c in a hyperbola

m = (plus or minus) a/b

The formula for the slopes of the asymptotes in a vertical hyperbola

m = (plus or minus) b/a

The formula for the slopes of the asymptotes in a horizontal hyperbola

Vertical (y is first)

Is this hyperbola vertical or horizontal? y^2/4 - x^2/16 = 1

Vertices are (5, 0) and (-5, 0)

What are the vertices in this hyperbola? x^2/25 - y^2/9 = 1

What are the slopes of the asymptotes? x^2/36 - y^2/100 = 1

This is a horizontal hyperbola so we use b/a which is 10/6 or 5/3 (+ and -)

Where are the foci in this hyperbola? y^2/36 - x^2/64 = 1

First, a^2 + b^2 = 100, so c = 10. Since this is a vertical hyperbola (y is first), the foci are (0, 10) and (0, -10)

Circle

r= asin(theta)

Parabola

the graph of a quadratic function

Ellipse

Equation adds x²/a² and y²/b²=1

Hyperbola

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

Line

A straight path that goes without end in two directions.

horizontal ellipse equation

(x-h)2/a2 + (y-k)2/b2 = 1

h+-a, k

horizontal ellipse & hyperbola vertices

h+-c, k

horizontal ellipse & hyperbola foci

c2=a2-b2

ellipse a2 b2 c2 equation

vertical ellipse equation

(x-h)2/b2 + (y-k)2/a2 = 1

h, k+-a

vertical ellipse & hyperbola vertices

h, k+-c

vertical ellipse & hyperbola foci

horizontal hyperbola equation

(x-h)2/a2 - (y-k)2/b2 = 1

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

horizontal hyperbola asymptotes

c2=a2+b2

hyperbola a2 b2 c2 equation

vertical hyperbola equation

(y-k)2/a2 - (x-h)2/b2= 1

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

vertical hyperbola asymptotes

Positive

Counting from the decimal point to the right makes the exponent ___________________________________________

bigger

ellipse a2 always...

circle equation

(x-h)2 + (y-k)2 = r2

(x-h)2 = 4p(y-k)

vertical parabola equation

h, k+p

vertical parabola focus

y=k-p

vertical parabola directrix

(y-k)2 = 4p(x-h)

horizontal parabola equation

h+p, k

horizontal parabola focus

x=h-p

horizontal parabola directrix

Ax²+By²+Cx+Dy+E=0

General equation for ellipse