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Categorizing Conics
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Inverts your trig
How triangles change
How is this relevant?
100

Classify the following conic as circle, ellipse, parabola, hyperbola

(x-2)2/4-(y+3)2/4=1

Hyperbola

100

The focal length of a circle

 0

100

name the pairs of inverse trig functions whose derivatives are the opposite signs of the other.

arcsin(x) and arccos(x)

arctan(x) and arccot(x)

arcsec(x) and arccsc(x)

100

the derivatives of sin(x), tan(x) and cot(x)

cos(x), sec2(x), -csc2(x)

100

An object trapped in orbit around a massive body with follow the path of this shape

what is an ellipse

200

Given these descriptions what type of conic is this?

foci at (-1,3) and (-5,3) and vertices at (0,3) and (-6,3) 

Ellipse

200

Lines parallel to the axis of symmetry of a parabola reflect towards this point

the focal point

200

the derivative of arcsin(3x)

3/sqrt(1-9x2)

200

Find the derivative

sec2(x)+sin2(x)+cos2(x)

2sec2(x)tan(x)

200

In order to collect a large amount of information or signal and direct it to a small point, many receivers have the shape of this curve

What is a parabola

300

Classify the following general form conic section

 x2+4x+y2-8y+12=0

Circle!

300

This conic section only has one focal point

Parabola

300
the derivative of arcsec(4/x)

1/(|4/x|sqrt(16/x2-1))(-4/x2)

300
Your speed in the y direction when you run around the edge of the unit circle 10 times per second when you are at theta=pi/6

10*sqrt(3)*pi

300

When you hear a sound, the delay between your two ears tells you that it occurred along this curve

What is a hyperbola

400

This type of conic has its standard form equation equal to zero

What is a degenerate conic

400

the focus points of the ellipse with a=8 in the horizontal direction, center at (1,1) and eccentricity of .75

(7,1) and (-5,1)

400

the derivative of arctan(sin(x))

cos(x)/(1+sin2(x))

400

the second derivative of cot(x)

2csc2(x)cot(x)

400

We can tell wether an object passing by the sun is from within the solar system or from the further regions of space by looking at this aspect of its trajectory.

What is the eccentricity

500

Given the general conic equation Ax2+Cy2+Dx+Ey+F=0 Under what condition is the conic section a Parabola.

A=0 or C=0

500

The focal length of the following conic section: 

4x2-y2+8x-6y+4=0

c=3.354

500

the derivative of sin(arcsin(sin(arcsin(sin(arcsin(x))))))

1
500

the lower angle of a right triangle is increasing at a rate of 2 rad/s. What is the rate of change of the slope of the hypotenuse when theta=pi/4

4/s

500

To find the best place to sit in the movie theater that will optimize the viewing angle of the screen, you will use this class of functions and derivative 

What is inverse trig derivatives/functions