Chapter 5

Question 1

Conic Sections

Answer 1

The shape that results from cutting through a cone

Question 2

Circles

Answer 2

Form when you cut straight across

Fromula: (x-h)^2 + (y-k)^2 = r^2

(h,k) = coordinates of the center
r = radius

Question 3

Ellipse

Answer 3

A stretched out circle

(x-h)^2/Rx^2 + (y-k)^2/Ry^2 = 1

(h.k) = center
Rx = Radius in x-direction
Ry = Radius in y-direction

Question 4

Parabola

Answer 4

An arc

Fromula for up/down: (x-h)^2 = 4p(y-k)
Left right: (y-k)^2 = 4p(x-h)

h,k,p = point around which the parabola arcs

up/down= (h, k+p)
left/right (h+k, p)

Question 5

Polar coordinates

Answer 5

A set of values that quantify the location of a point based on the distance to a fixed origin and the angle in between.

Denoted by (R, Theta)

Question 6

Cartesian coordinates

Answer 6

(x,y)

Question 7

Cartesian —–> polar steps

Answer 7

1). Use Pythagorean theorem to find r
2). use inverse trig to find theta. {tan-1(y/x), Sin-1(y/r), Cos_1(x/r)}

Question 8

Quadrant table for Polar and cartesian coordinates

Answer 8

Quadrant
Cartesian
Theta Range
1
(X,Y)
0-90
2
(-X,Y)
90-180
3
(-X,-Y)
180-270
4
(X,-Y)
270-360

**Must make sure the angle you get matches its quadrant. If not use table to adjust.

Question 9

Polar —–> Cartesian

Answer 9

x=r.cos(theta)
y=r.sin(theta)

**Make sure angle matches coordinates

Question 10

Quad 2and3 adjustments formula

Answer 10

2- 180-tan-1(y/x)
3- 180+tan-1(y/x)